Subjects -> MATHEMATICS (Total: 1118 journals)
    - APPLIED MATHEMATICS (92 journals)
    - GEOMETRY AND TOPOLOGY (23 journals)
    - MATHEMATICS (819 journals)
    - MATHEMATICS (GENERAL) (45 journals)
    - NUMERICAL ANALYSIS (26 journals)
    - PROBABILITIES AND MATH STATISTICS (113 journals)

MATHEMATICS (819 journals)                  1 2 3 4 5 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 5)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 3)
Accounting Perspectives     Full-text available via subscription   (Followers: 9)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 17)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 5)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 9)
ACS Applied Materials & Interfaces     Hybrid Journal   (Followers: 44)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 2)
Acta Mathematica     Hybrid Journal   (Followers: 11)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 6)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 13)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 6)
Advances in Catalysis     Full-text available via subscription   (Followers: 8)
Advances in Complex Systems     Hybrid Journal   (Followers: 12)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 23)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 5)
Advances in Fixed Point Theory     Open Access   (Followers: 9)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 22)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 10)
Advances in Materials Science     Open Access   (Followers: 22)
Advances in Mathematical Physics     Open Access   (Followers: 10)
Advances in Mathematics     Full-text available via subscription   (Followers: 22)
Advances in Numerical Analysis     Open Access   (Followers: 8)
Advances in Operations Research     Open Access   (Followers: 14)
Advances in Operator Theory     Hybrid Journal   (Followers: 4)
Advances in Porous Media     Full-text available via subscription   (Followers: 6)
Advances in Pure Mathematics     Open Access   (Followers: 11)
Advances in Science and Research (ASR)     Open Access   (Followers: 8)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 12)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 7)
Afrika Matematika     Hybrid Journal   (Followers: 3)
Air, Soil & Water Research     Open Access   (Followers: 13)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 4)
AKSIOMATIK : Jurnal Penelitian Pendidikan dan Pembelajaran Matematika     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access   (Followers: 1)
Al-Qadisiyah Journal for Computer Science and Mathematics     Open Access   (Followers: 1)
AL-Rafidain Journal of Computer Sciences and Mathematics     Open Access   (Followers: 6)
Algebra and Logic     Hybrid Journal   (Followers: 8)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Open Access   (Followers: 5)
Algorithms     Open Access   (Followers: 14)
Algorithms Research     Open Access   (Followers: 2)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 10)
American Journal of Mathematical Analysis     Open Access   (Followers: 2)
American Journal of Mathematical and Management Sciences     Hybrid Journal   (Followers: 1)
American Journal of Mathematics     Full-text available via subscription   (Followers: 9)
American Journal of Operations Research     Open Access   (Followers: 8)
American Mathematical Monthly     Full-text available via subscription   (Followers: 7)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 13)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access  
Analysis and Applications     Hybrid Journal   (Followers: 2)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 10)
Analysis Mathematica     Full-text available via subscription  
Anargya : Jurnal Ilmiah Pendidikan Matematika     Open Access   (Followers: 8)
Annales Mathematicae Silesianae     Open Access   (Followers: 2)
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 17)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 8)
Annals of Functional Analysis     Hybrid Journal   (Followers: 4)
Annals of Mathematics     Full-text available via subscription   (Followers: 4)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 16)
Annals of PDE     Hybrid Journal  
Annals of Pure and Applied Logic     Open Access   (Followers: 6)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access   (Followers: 1)
Annals of West University of Timisoara - Mathematics and Computer Science     Open Access   (Followers: 2)
Annuaire du Collège de France     Open Access   (Followers: 6)
ANZIAM Journal     Open Access   (Followers: 2)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 3)
Applications of Mathematics     Hybrid Journal   (Followers: 3)
Applied Categorical Structures     Hybrid Journal   (Followers: 4)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 16)
Applied Mathematics     Open Access   (Followers: 10)
Applied Mathematics     Open Access   (Followers: 6)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 13)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal   (Followers: 2)
Applied Mathematics and Nonlinear Sciences     Open Access   (Followers: 1)
Applied Mathematics Letters     Full-text available via subscription   (Followers: 3)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 2)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 6)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 6)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 4)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 4)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 6)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 6)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Armenian Journal of Mathematics     Open Access   (Followers: 1)
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites     Open Access   (Followers: 24)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Research Journal of Mathematics     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 4)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 7)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 2)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access   (Followers: 1)
Baltic International Yearbook of Cognition, Logic and Communication     Open Access   (Followers: 2)
Banach Journal of Mathematical Analysis     Hybrid Journal   (Followers: 1)
Basin Research     Hybrid Journal   (Followers: 6)
BIBECHANA     Open Access   (Followers: 2)
Biomath     Open Access  
BIT Numerical Mathematics     Hybrid Journal   (Followers: 1)
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 3)
British Journal for the History of Mathematics     Hybrid Journal  
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 20)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 15)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 3)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 3)
Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics     Open Access  
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 2)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the Iranian Mathematical Society     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Cadernos do IME : Série Matemática     Open Access   (Followers: 2)
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Mathematics / Journal canadien de mathématiques     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 23)
Canadian Mathematical Bulletin     Hybrid Journal  
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 6)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
Chaos, Solitons & Fractals : X     Open Access   (Followers: 1)
ChemSusChem     Hybrid Journal   (Followers: 8)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 3)
Chinese Journal of Mathematics     Open Access  
Ciencia     Open Access   (Followers: 1)
CODEE Journal     Open Access   (Followers: 2)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 3)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Hybrid Journal   (Followers: 4)
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 17)
Commentarii Mathematici Helvetici     Hybrid Journal  
Communications in Advanced Mathematical Sciences     Open Access  
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 4)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 5)
Complex Analysis and its Synergies     Open Access   (Followers: 3)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Composite Materials Series     Full-text available via subscription   (Followers: 11)
Compositio Mathematica     Full-text available via subscription  
Comptes Rendus : Mathematique     Open Access  
Computational and Applied Mathematics     Hybrid Journal   (Followers: 4)
Computational and Mathematical Methods     Hybrid Journal  
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 3)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 1)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 9)
Computational Mechanics     Hybrid Journal   (Followers: 10)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 11)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 11)
Confluentes Mathematici     Hybrid Journal  
Constructive Mathematical Analysis     Open Access   (Followers: 1)
Contributions to Discrete Mathematics     Open Access   (Followers: 1)
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal   (Followers: 1)
Cryptography and Communications     Hybrid Journal   (Followers: 14)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 8)
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Daya Matematis : Jurnal Inovasi Pendidikan Matematika     Open Access   (Followers: 1)
Demographic Research     Open Access   (Followers: 16)
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 35)
Desimal : Jurnal Matematika     Open Access   (Followers: 3)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 4)

        1 2 3 4 5 | Last

Similar Journals
Journal Cover
Arnold Mathematical Journal
Journal Prestige (SJR): 0.355
Number of Followers: 1  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 2199-6792 - ISSN (Online) 2199-6806
Published by Springer-Verlag Homepage  [2658 journals]
  • Varieties in Cages: A Little Zoo of Algebraic Geometry

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      Abstract: Abstract A \(d^{\{n\}}\) -cage \(\mathsf K\) is the union of n groups of hyperplanes in \(\mathbb P^n\) , each group containing d members. The hyperplanes from the distinct groups are in general position, thus producing \(d^n\) points where hyperplanes from all groups intersect. These points are called the nodes of \(\mathsf K\) . We study the combinatorics of nodes that impose independent conditions on the varieties \(X \subset \mathbb P^n\) containing them. We prove that if X, given by homogeneous polynomials of degrees \(\le d\) , contains the points from such a special set \(\mathsf A\) of nodes, then it contains all the nodes of \(\mathsf K\) . Such a variety X is very special: in particular, X is a complete intersection.
      PubDate: 2021-09-30
       
  • An Extension of the $$\mathfrak {sl}_2$$ sl 2 Weight System to Graphs with
           $$n \le 8$$ n ≤ 8 Vertices

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      Abstract: Abstract Chord diagrams and 4-term relations were introduced by Vassiliev in the late 1980. Various constructions of weight systems are known, and each of such constructions gives rise to a knot invariant. In particular, weight systems may be constructed from Lie algebras as well as from the so-called 4-invariants of graphs. A Chmutov–Lando theorem states that the value of the weight system constructed from the Lie algebra \(\mathfrak {sl}_2\) on a chord diagram depends on the intersection graph of the diagram, rather than the diagram itself. This inspired a question due to Lando about whether it is possible to extend the weight system \(\mathfrak {sl}_2\) to a graph invariant satisfying the four term relations for graphs. We show that for all graphs with up to 8 vertices such an extension exists and is unique, thus answering in affirmative to Lando’s question for small graphs.
      PubDate: 2021-09-06
       
  • Integrability of Point-Vortex Dynamics via Symplectic Reduction: A Survey

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      Abstract: Abstract Point-vortex dynamics describe idealized, non-smooth solutions to the incompressible Euler equations on two-dimensional manifolds. Integrability results for few point-vortices on various domains is a vivid topic, with many results and techniques scattered in the literature. Here, we give a unified framework for proving integrability results for \(N=2\) , 3, or 4 point-vortices (and also more general Hamiltonian systems), based on symplectic reduction theory. The approach works on any two-dimensional manifold with a symmetry group; we illustrate it on the sphere, the plane, the hyperbolic plane, and the flat torus. A systematic study of integrability is prompted by advances in two-dimensional turbulence, bridging the long-time behaviour of 2D Euler equations with questions of point-vortex integrability. A gallery of solutions is given in the appendix.
      PubDate: 2021-09-01
       
  • Inflation of Poorly Conditioned Zeros of Systems of Analytic Functions

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      Abstract: Abstract Given a system of analytic functions and an approximate zero, we introduce inflation to transform this system into one with a regular quadratic zero. This leads to a method for isolating a cluster of zeros of the given system.
      PubDate: 2021-09-01
       
  • Interpolation of Weighted Extremal Functions

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      Abstract: Abstract An approach to interpolation of compact subsets of \({{\mathbb {C}}}^n\) , including Brunn–Minkowski type inequalities for the capacities of the interpolating sets, was developed in [8] by means of plurisubharmonic geodesics between relative extremal functions of the given sets. Here we show that a much better control can be achieved by means of the geodesics between weighted relative extremal functions. In particular, we establish convexity properties of the capacities that are stronger than those given by the Brunn–Minkowski inequalities.
      PubDate: 2021-09-01
       
  • Remarks on Joachimsthal Integral and Poritsky Property

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      Abstract: Abstract The billiard in an ellipse has a conserved quantity, the Joachimsthal integral. We show that the existence of such an integral characterizes conics. We extend this result to the spherical and hyperbolic geometries and to higher dimensions. We connect the existence of Joachimsthal integral with the Poritsky property, a property of billiard curves, called so after H. Poritsky whose important paper Poritsky (Ann Math 51:446–470, 1950) was one of the early studies of the billiard problem.
      PubDate: 2021-09-01
       
  • Conjectures on Stably Newton Degenerate Singularities

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      Abstract: Abstract We discuss a problem of Arnold, whether every function is stably equivalent to one which is non-degenerate for its Newton diagram. We argue that the answer is negative. We describe a method to make functions non-degenerate after stabilisation and give examples of singularities where this method does not work. We conjecture that they are in fact stably degenerate, that is not stably equivalent to non-degenerate functions. We review the various non-degeneracy concepts in the literature. For finite characteristic, we conjecture that there are no wild vanishing cycles for non-degenerate singularities. This implies that the simplest example of singularities with finite Milnor number, \(x^p+x^q\) in characteristic p, is not stably equivalent to a non-degenerate function. We argue that irreducible plane curves with an arbitrary number of Puiseux pairs (in characteristic zero) are stably non-degenerate. As the stabilisation involves many variables, it becomes very difficult to determine the Newton diagram in general, but the form of the equations indicates that the defining functions are non-degenerate.
      PubDate: 2021-09-01
       
  • The Yomdin–Gromov Algebraic Lemma Revisited

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      Abstract: Abstract In 1987, Yomdin proved a lemma on smooth parametrizations of semialgebraic sets as part of his solution of Shub’s entropy conjecture for \(C^\infty \) maps. The statement was further refined by Gromov, producing what is now known as the Yomdin–Gromov algebraic lemma. Several complete proofs based on Gromov’s sketch have appeared in the literature, but these have been considerably more complicated than Gromov’s original presentation due to some technical issues. In this note, we give a proof that closely follows Gromov’s original presentation. We prove a somewhat stronger statement, where the parametrizing maps are guaranteed to be cellular. It turns out that this additional restriction, along with some elementary lemmas on differentiable functions in o-minimal structures, allows the induction to be carried out without technical difficulties.
      PubDate: 2021-09-01
       
  • On the Density of Dispersing Billiard Systems with Singular Periodic
           Orbits

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      Abstract: Abstract Dynamical billiards, or the behavior of a particle traveling in a planar region D undergoing elastic collisions with the boundary has been extensively studied and is used to model many physical phenomena such as a Boltzmann gas. Of particular interest are the dispersing billiards, where D consists of a union of finitely many open convex regions. These billiard flows are known to be ergodic and to possess the K-property. However, Turaev and Rom-Kedar proved that for dispersing systems permitting singular periodic orbits, there exists a family of smooth Hamiltonian flows with regions of stability near such orbits, converging to the billiard flow. They conjecture that systems possessing such singular periodic orbits are dense in the space of all dispersing billiard systems and remark that if this conjecture is true then every dispersing billiard system is arbitrarily close to a non-ergodic smooth Hamiltonian flow with regions of stability [6]. We present a partial solution to this conjecture by showing that any system with a near-singular periodic orbit satisfying certain conditions can be perturbed to a system that permits a singular periodic orbit. We comment on the assumptions of our theorem that must be removed to prove the conjecture of Turaev and Rom-Kedar.
      PubDate: 2021-09-01
       
  • Fifty New Invariants of N-Periodics in the Elliptic Billiard

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      Abstract: Abstract We introduce 50+ new invariants manifested by the dynamic geometry of N-periodics in the Elliptic Billiard, detected with an experimental/interactive toolbox. These involve sums, products and ratios of distances, areas, angles, etc. Though curious in their manifestation, said invariants do all depend upon the two fundamental conserved quantities in the Elliptic Billiard: perimeter and Joachimsthal’s constant. Several proofs have already been contributed (references are provided); these have mainly relied on algebraic geometry. We very much welcome new proofs and contributions.
      PubDate: 2021-09-01
       
  • A Galois–Dynamics Correspondence for Unicritical Polynomials

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      Abstract: Abstract In an analogy with the Galois homothety property for torsion points of abelian varieties that was used in the proof of the Mordell–Lang conjecture, we describe a correspondence between the action of a Galois group and the dynamical action of a rational map. For nonlinear polynomials with rational coefficients, the irreducibility of the associated dynatomic polynomial serves as a convenient criterion, although we also verify that the correspondence occurs in several cases when the dynatomic polynomial is reducible. The work of Morton, Morton–Patel, and Vivaldi–Hatjispyros in the early 1990s connected the irreducibility and Galois-theoretic properties of dynatomic polynomials to rational periodic points; from the Galois–dynamics correspondence, we derive similar consequences for quadratic periodic points of unicritical polynomials. This is sufficient to deduce the non-existence of quadratic periodic points of quadratic polynomials with exact period 5 and 6, outside of a specified finite set from Morton and Krumm’s work in explicit Hilbert irreducibility.
      PubDate: 2021-09-01
       
  • Element-Building Games on $$\mathbb {Z}_n$$ Z n

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      Abstract: Abstract We consider a pair of games where two players alternately select previously unselected elements of \(\mathbb {Z}_n\) given a particular starting element. On each turn, the player either adds or multiplies the element they selected to the result of the previous turn. In one game, the first player wins if the final result is 0; in the other, the second player wins if the final result is 0. We determine which player has the winning strategy for both games except for the latter game with nonzero starting element when \(n \in \{2p,4p\}\) for some odd prime p.
      PubDate: 2021-08-18
       
  • New Invariants of Poncelet–Jacobi Bicentric Polygons

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      Abstract: Abstract The 1d family of Poncelet polygons interscribed between two circles is known as the Bicentric family. Using elliptic functions and Liouville’s theorem, we show (i) that this family has invariant sum of internal angle cosines and (ii) that the pedal polygons with respect to the family’s limiting points have invariant perimeter. Interestingly, both (i) and (ii) are also properties of elliptic billiard N-periodics. Furthermore, since the pedal polygons in (ii) are identical to inversions of elliptic billiard N-periodics with respect to a focus-centered circle, an important corollary is that (iii) elliptic billiard focus-inversive N-gons have constant perimeter. Interestingly, these also conserve their sum of cosines (except for the \(N=4\) case).
      PubDate: 2021-08-18
       
  • Cutpoints of Invariant Subcontinua of Polynomial Julia Sets

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      Abstract: Abstract We prove fixed point results for branched covering maps f of the plane. For complex polynomials P with Julia set \(J_{P}\) these imply that periodic cutpoints of some invariant subcontinua of \(J_{P}\) are also cutpoints of \(J_{P}\) . We deduce that, under certain assumptions on invariant subcontinua Q of \(J_{P}\) , every Riemann ray to Q landing at a periodic repelling/parabolic point \(x\in Q\) is isotopic to a Riemann ray to \(J_{P}\) relative to Q.
      PubDate: 2021-08-16
       
  • Surfaces of Section for Seifert Fibrations

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      Abstract: Abstract We classify global surfaces of section for flows on 3-manifolds defining Seifert fibrations. We discuss branched coverings—one way or the other—between surfaces of section for the Hopf flow and those for any other Seifert fibration of the 3-sphere, and we relate these surfaces of section to algebraic curves in weighted complex projective planes.
      PubDate: 2021-08-05
       
  • On a Theorem of Lyapunov–Poincaré in Higher Dimensions

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      Abstract: Abstract The classical Lyapunov–Poincaré center theorem assures the existence of a first integral for an analytic 1-form near a center singularity in dimension two, provided that the first jet of the 1-form is nondegenerate. The basic point is the existence of an analytic first integral for the given 1-form. In this paper, we consider generalizations for two main frameworks: (1) real analytic foliations of codimension one in higher dimension and (2) singular holomorphic foliations in dimension two. All this is related to the problem of finding criteria assuring the existence of analytic first integrals for a given codimension one germ with a suitable first jet. Our approach consists in giving an interpretation of the center theorem in terms of holomorphic foliations and, following an idea of Moussu, apply the holomorphic foliations arsenal to obtain the required first integral. As a consequence we are able to revisit some of Reeb’s classical results on integrable perturbations of exact homogeneous 1-forms, and prove versions of these in the framework of non-isolated (perturbations of transversely Morse type) singularities.
      PubDate: 2021-07-13
       
  • Real Lines on Random Cubic Surfaces

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      Abstract: Abstract We give an explicit formula for the expectation of the number of real lines on a random invariant cubic surface, i.e., a surface \(Z\subset {\mathbb {R}}{\mathrm {P}}^3\) defined by a random gaussian polynomial whose probability distribution is invariant under the action of the orthogonal group O(4) by change of variables. Such invariant distributions are completely described by one parameter \(\lambda \in [0,1]\) and as a function of this parameter the expected number of real lines equals: $$\begin{aligned} E_\lambda =\frac{9(8\lambda ^2+(1-\lambda )^2)}{2\lambda ^2+(1-\lambda )^2}\left( \frac{2\lambda ^2}{8\lambda ^2+(1-\lambda )^2}-\frac{1}{3}+\frac{2}{3}\sqrt{\frac{8\lambda ^2+(1-\lambda )^2}{20\lambda ^2+(1-\lambda )^2}}\right) . \end{aligned}$$ This result generalizes previous results by Basu et al. (Math Ann 374(3–4):1773–1810, 2019) for the case of a Kostlan polynomial, which corresponds to \(\lambda =\frac{1}{3}\) and for which \(E_{\frac{1}{3}}=6\sqrt{2}-3.\) Moreover, we show that the expectation of the number of real lines is maximized by random purely harmonic cubic polynomials, which corresponds to the case \(\lambda =1\) and for which \(E_1=24\sqrt{\frac{2}{5}}-3\) .
      PubDate: 2021-07-02
       
  • Strange Duality Between the Quadrangle Complete Intersection Singularities

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      Abstract: Abstract There is a strange duality between the quadrangle isolated complete intersection singularities discovered by the first author and Wall. We derive this duality from a variation of the Berglund–Hübsch transposition of invertible polynomials introduced in our previous work about the strange duality between hypersurface and complete intersection singularities using matrix factorizations of size two.
      PubDate: 2021-06-22
       
  • Simplicity of Spectra for Bethe Subalgebras in $${\mathrm {Y}}({\mathfrak
           {gl}}_2)$$ Y ( gl 2 )

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      Abstract: Abstract We consider Bethe subalgebras B(C) in the Yangian \({\mathrm {Y}}({\mathfrak {gl}}_2)\) with C regular \(2\times 2\) matrix. We study the action of Bethe subalgebras of \({\mathrm {Y}}({\mathfrak {gl}}_2)\) on finite-dimensional representations of \({\mathrm {Y}}({\mathfrak {gl}}_2)\) . We prove that B(C) with real diagonal C has simple spectrum on any irreducible \({\mathrm {Y}}({\mathfrak {gl}}_2)\) -module corresponding to a disjoint union of real strings. We extend this result to limits of Bethe algebras. Our main tool is the computation of Shapovalov-type determinant for the nilpotent degeneration of B(C).
      PubDate: 2021-06-01
       
  • Probabilistic Schubert Calculus: Asymptotics

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      Abstract: Abstract In the recent paper Bürgisser and Lerario (Journal für die reine und angewandte Mathematik (Crelles J), 2016) introduced a geometric framework for a probabilistic study of real Schubert Problems. They denoted by \(\delta _{k,n}\) the average number of projective k-planes in \({\mathbb {R}}\mathrm {P}^n\) that intersect \((k+1)(n-k)\) many random, independent and uniformly distributed linear projective subspaces of dimension \(n-k-1\) . They called \(\delta _{k,n}\) the expected degree of the real Grassmannian \({\mathbb {G}}(k,n)\) and, in the case \(k=1\) , they proved that: $$\begin{aligned} \delta _{1,n}= \frac{8}{3\pi ^{5/2}} \cdot \left( \frac{\pi ^2}{4}\right) ^n \cdot n^{-1/2} \left( 1+{\mathcal {O}}\left( n^{-1}\right) \right) . \end{aligned}$$ Here we generalize this result and prove that for every fixed integer \(k>0\) and as \(n\rightarrow \infty \) , we have $$\begin{aligned} \delta _{k,n}=a_k \cdot \left( b_k\right) ^n\cdot n^{-\frac{k(k+1)}{4}}\left( 1+{\mathcal {O}}(n^{-1})\right) \end{aligned}$$ where \(a_k\) and \(b_k\) are some (explicit) constants, and \(a_k\) involves an interesting integral over the space of polynomials that have all real roots. For instance: $$\begin{aligned} \delta _{2,n}= \frac{9\sqrt{3}}{2048\sqrt{2\pi }} \cdot 8^n \cdot n^{-3/2} \left( 1+{\mathcal {O}}\left( n^{-1}\right) \right) . \end{aligned}$$ Moreover we prove that these numbers belong to the ring of periods intoduced by Kontsevich and Zagier and give an explicit formula for \(\delta _{1,n}\) involving a one-dimensional integral of certain combination of Elliptic functions.
      PubDate: 2021-06-01
       
 
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