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 Bulletin of the Brazilian Mathematical Society, New Series   [SJR: 0.436]   [H-I: 19]   [0 followers]  Follow         Hybrid journal (It can contain Open Access articles)    ISSN (Print) 1678-7544 - ISSN (Online) 1678-7714    Published by Springer-Verlag  [2329 journals]
• Sectional Anosov Flows: Existence of Venice Masks with Two Singularities
• Authors: Andrés M. López Barragán; Henry M. S. Sánchez
Pages: 1 - 18
Abstract: We show the existence of Venice masks (i.e. nontransitive sectional Anosov flows with dense periodic orbits, Bautista and Morales http://preprint.impa.br/Shadows/SERIE_D/2011/86.html; Bautista et al. Discr Contin Dyn Syst 19(4):761, 2007; Morales and Pacífico Pac J Math 216(2):327–342, 2004, Morales et al. Pac J Math 229(1):223–232, 2007) containing two equilibria on certain compact 3-manifolds. Indeed, we present two type of examples in which the homoclinic classes composing their maximal invariant set intersect in a very different way.
PubDate: 2017-03-01
DOI: 10.1007/s00574-016-0015-7
Issue No: Vol. 48, No. 1 (2017)

• Compact Invariant Sets for Global Holomorhic Foliations
• Authors: Arturo Fernández-Pérez; Rogério Mol; Rudy Rosas
Pages: 19 - 28
Abstract: We study compact invariant sets for holomorphic foliations on Stein manifold. As application, we show some dynamical properties concerning minimal sets (with singularities) of foliations and real analytic Levi-flat hypersurfaces in projective spaces.
PubDate: 2017-03-01
DOI: 10.1007/s00574-016-0012-x
Issue No: Vol. 48, No. 1 (2017)

• Stability Of Branched Pull-Back Projective Foliations
• Authors: W. Costa e Silva
Pages: 29 - 44
Abstract: We present new irreducible components of the space of codimension one holomorphic foliations on $$\mathbb P^{n}$$ , $$n\ge 3$$ . They are associated to pull-back by branched rational maps of foliations on $$\mathbb P^2$$ that preserve invariant lines.
PubDate: 2017-03-01
DOI: 10.1007/s00574-016-0007-7
Issue No: Vol. 48, No. 1 (2017)

• Uniqueness of Spacelike Hypersurfaces in a GRW Spacetime via Higher Order
Mean Curvatures
• Authors: Cícero P. Aquino; Jogli G. Araújo; Márcio Batista; Henrique F. de Lima
Pages: 45 - 61
Abstract: We study the problem of uniqueness concerning complete spacelike hypersurfaces immersed in a generalized Robertson–Walker (GRW) spacetime, whose fiber obeys suitable curvature constraints. In this setting, we apply some maximum principles in order to guarantee that such a spacelike hypersurface must be a slice of the ambient space, provided that some of their higher order mean curvatures satisfies appropriated controls. Furthermore, we also establish nonparametric results concerning entire spacelike graphs in GRW spacetimes.
PubDate: 2017-03-01
DOI: 10.1007/s00574-016-0004-x
Issue No: Vol. 48, No. 1 (2017)

• Bounded Limit Cycles of Polynomial Foliations of $$\mathbb {C}^{2}$$ C 2
• Authors: Nataliya Goncharuk; Yury Kudryashov
Pages: 63 - 83
Abstract: In this article we prove in a new way that a generic polynomial vector field in $$\mathbb {C}^{2}$$ possesses countably many homologically independent limit cycles. The new proof needs no estimates on integrals, provides thinner exceptional set for quadratic vector fields, and provides limit cycles that stay in a bounded domain.
PubDate: 2017-03-01
DOI: 10.1007/s00574-016-0005-9
Issue No: Vol. 48, No. 1 (2017)

• Foliations on Modular Curves
• Authors: Igor V. Nikolaev
Pages: 85 - 92
Abstract: It is proved, that a foliation on a modular curve given by the vertical trajectories of holomorphic differential corresponding to the Hecke eigenform is either the Strebel foliation or the pseudo-Anosov foliation.
PubDate: 2017-03-01
DOI: 10.1007/s00574-016-0006-8
Issue No: Vol. 48, No. 1 (2017)

• Points on singular Frobenius nonclassical curves
• Authors: Herivelto Borges; Masaaki Homma
Pages: 93 - 101
Abstract: In 1990, Hefez and Voloch proved that the number of $$\mathbb {F}_q$$ -rational points on a nonsingular plane q-Frobenius nonclassical curve of degree d is $$N=d(q-d+2)$$ . We address these curves in the singular setting. In particular, we prove that $$d(q-d+2)$$ is a lower bound on the number of $$\mathbb {F}_q$$ -rational points on such curves of degree d.
PubDate: 2017-03-01
DOI: 10.1007/s00574-016-0008-6
Issue No: Vol. 48, No. 1 (2017)

• Positive Neighborhoods of Rational Curves
• Authors: M. Falla Luza; P. Sad
Pages: 103 - 110
Abstract: We study neighborhoods of rational curves in surfaces with self-intersection number 1 that can be linearised.
PubDate: 2017-03-01
DOI: 10.1007/s00574-016-0009-5
Issue No: Vol. 48, No. 1 (2017)

• On Weakly Hyperbolic Iterated Function Systems
• Authors: Alexander Arbieto; André Junqueira; Bruno Santiago
Pages: 111 - 140
Abstract: We study weakly hyperbolic iterated function systems on compact metric spaces, as defined by Edalat (Inform Comput 124(2):182–197, 1996), but in the more general setting of compact parameter space. We prove the existence of attractors, both in the topological and measure theoretical viewpoint and the ergodicity of invariant measure. We also define weakly hyperbolic iterated function systems for complete metric spaces and compact parameter space, extending the above mentioned definition. Furthermore, we study the question of existence of attractors in this setting. Finally, we prove a version of the results by Barnsley and Vince (Ergodic Theory Dyn Syst 31(4):1073–1079, 2011), about drawing the attractor (the so-called the chaos game), for compact parameter space.
PubDate: 2017-03-01
DOI: 10.1007/s00574-016-0018-4
Issue No: Vol. 48, No. 1 (2017)

• On the Constants of the Bohnenblust–Hille and Hardy–Littlewood
Inequalities
• Authors: Gustavo Araújo; Daniel Pellegrino
Pages: 141 - 169
Abstract: For $$\mathbb {K}=\mathbb {R}$$ or $$\mathbb {C}$$ , the Hardy–Littlewood inequality for m-linear forms asserts that for $$4\le 2m\le p\le \infty$$ there exists a constant $$C_{m,p}^{\mathbb {K}}\ge 1$$ such that, for all m-linear forms $$T:\ell _{p}^{n}\times \cdots \times \ell _{p}^{n}\rightarrow \mathbb {K}$$ , and all positive integers n, This result was proved by Hardy and Littlewood (QJ Math 5:241–254, 1934) for bilinear forms and extended to m-linear forms by Praciano-Pereira (J Math Anal Appl 81:561–568, 1981). The case $$p=\infty$$ recovers the Bohnenblust–Hille inequality (Ann Math 32:600–622, 1931). In this paper, among other results, we show that for $$p>2m(m-1)^2$$ the optimal constants satisfying the Hardy–Littlewood inequality for m-linear forms are dominated by the best known constants of the corresponding Bohnenblust–Hille inequality. For instance, we show that if $$p>2m(m-1)^2$$ , then \begin{aligned} \textstyle C_{m,p}^{\mathbb {C}}\le \prod \limits _{j=2}^{m}\Gamma \left( 2-\frac{1}{j}\right) ^{\frac{j}{2-2j}}<m^{\frac{1-\gamma }{2}}, \end{aligned} where $$\gamma$$ is the Euler–Mascheroni constant.
PubDate: 2017-03-01
DOI: 10.1007/s00574-016-0016-6
Issue No: Vol. 48, No. 1 (2017)

• Sharp Constant of an Anisotropic Gagliardo–Nirenberg-Type Inequality
and Applications
• Authors: Amin Esfahani; Ademir Pastor
Pages: 171 - 185
Abstract: In this paper we establish the best constant of an anisotropic Gagliardo–Nirenberg-type inequality related to the Benjamin–Ono–Zakharov–Kuznetsov equation. As an application of our results, we prove the uniform bound of solutions for such a equation in the energy space.
PubDate: 2017-03-01
DOI: 10.1007/s00574-016-0017-5
Issue No: Vol. 48, No. 1 (2017)

• On Umbilic Points on Newly Born Surfaces
• Authors: Masaru Hasegawa; Farid Tari
Abstract: The simplest way to have birth of surfaces is through transitions in the fibres of a function f with a Morse singularity of index 0 or 3. It is natural to seek to understand the geometry of newly born surfaces. We consider here the question of finding how many umbilics are on a newly born surface. We show that newly born surfaces in the Euclidean 3-space have exactly 4 umbilic points all of type lemon, provided that the Hessian of f at the singular point has pairwise distinct eigenvalues. This is true in both cases when f is an analytic or a smooth germ. When only two of such eigenvalues are equal, the number of umbilic points is either 2, 4, 6 or 8 when f is an analytic or a generic smooth germ. The same results holds for newly born surfaces in the Minkowski 3-space. In that case when the two eigenvalues associated to the two spacelike eigenvectors are distinct we get exactly 4 umbilic points all of type lemon. If they are equal, the number of umbilic points is either 2, 4, 6 or 8.
PubDate: 2017-05-11
DOI: 10.1007/s00574-017-0037-9

• Classification of Jets of Surfaces in Projective 3-Space Via Central
Projection
• Authors: H. Sano; Y. Kabata; J. L. Deolindo Silva; T. Ohmoto
Abstract: We present a local classification of smooth surfaces in $${\mathbb {P}}^3$$ in terms of the singularity types (of codimension $$\le$$ 4) of their central projections to a plane. Based on our classification result, we also give exact normal forms to surface germs at transition moments on bifurcations with respect to parabolic curves and flecnodal curves.
PubDate: 2017-04-21
DOI: 10.1007/s00574-017-0036-x

• On Classical Uniformization Theorems for Higher Dimensional Complex
Kleinian Groups
• Authors: Angel Cano; Luis Loeza; Alejandro Ucan-Puc
Abstract: In this article we show that Bers’ simultaneous uniformization and Köebe’s retrosection theorem do not hold for discrete groups of projective transformations acting on complex projective space.
PubDate: 2017-04-13
DOI: 10.1007/s00574-017-0035-y

• Well-Posedness Results and Dissipative Limit of High Dimensional KdV-Type
Equations
• Authors: Xavier Carvajal; Amin Esfahani; Mahendra Panthee
Abstract: Considered in this work is an n-dimensional dissipative version of the Korteweg–de Vries (KdV) equation. Our goal here is to investigate the well-posedness issue for the associated initial value problem in the anisotropic Sobolev spaces. We also study well-posedness behavior of this equation when the dissipative effects are reduced.
PubDate: 2017-04-04
DOI: 10.1007/s00574-017-0034-z

• Properties of Shadowable Points: Chaos and Equicontinuity
• Authors: Noriaki Kawaguchi
Abstract: We extend the study on shadowable points recently introduced by Morales in relation to chaotic or non-chaotic properties. Firstly, some sufficient conditions for a quantitative shadowable point to be approximated by an entropy point are given. As a corollary, we get different three chaotic conditions from which a shadowable point becomes an entropy point. Secondly, we provide a dichotomy on the interior of the set of shadowable chain recurrent points by two canonical chaotic and non-chaotic dynamics, the full shift and odometers.
PubDate: 2017-03-24
DOI: 10.1007/s00574-017-0033-0

• Induced Hausdorff Metrics on Quotient Spaces
• Authors: Ryuichi Fukuoka; Djeison Benetti
Abstract: Let G be a group, (M, d) be a metric space, $$X\subset M$$ be a compact subset and $$\varphi :G\times M\rightarrow M$$ be a left action of G on M by homeomorphisms. Denote $$gp=\varphi (g,p)$$ . The isotropy subgroup of G with respect to X is defined by $$H_X=\{g\in G; gX=X\}$$ . In this work we define the induced Hausdorff metric on $$G/H_X$$ by $$d_X(g_1H_X,g_2H_X):=d_H(g_1X,g_2X)$$ , where $$d_H$$ is the Hausdorff distance on M. Let $$\hat{d}_X$$ be the intrinsic metric induced by $$d_X$$ . In this work, we study the geometry of $$(G/H_X,d_X)$$ and $$(G/H_X,\hat{d}_X)$$ and their relationship with (M, d). In particular, we prove that if G is a Lie group, M is a differentiable manifold endowed with a metric which is locally Lipschitz equivalent to a Finsler metric, $$X\subset M$$ is a compact subset and $$\varphi :G\times M\rightarrow M$$ is a smooth left action by isometries, then $$(G/H_X,\hat{d}_X)$$ is a $$C^0$$ -Finsler manifold. We also calculate the Finsler metric explicitly in some examples.
PubDate: 2017-03-22
DOI: 10.1007/s00574-017-0032-1

• Pontryagin’s Risk-Sensitive Stochastic Maximum Principle for Backward
Stochastic Differential Equations with Application
Abstract: This paper studies the risk-sensitive optimal control problem for a backward stochastic system. More precisely, we set up a necessary stochastic maximum principle for a risk-sensitive optimal control of this kind of equations. The control domain is assumed to be convex and the generator coefficient of such system is allowed to be depend on the control variable. As a preliminary step, we study the risk-neutral problem for which an optimal solution exists. This is an extension of initial control system to this type of problem, where the set of admissible controls is convex. An example to carried out to illustrate our main result of risk-sensitive control problem under linear stochastic dynamics with exponential quadratic cost function.
PubDate: 2017-02-23
DOI: 10.1007/s00574-017-0031-2

• Non-Homogeneous Thermoelastic Timoshenko Systems
• Authors: M. S. Alves; M. A. Jorge Silva; T. F. Ma; J. E. Muñoz Rivera
Abstract: The well-established Timoshenko system is characterized by a particular relation between shear stress and bending moment from its constitutive equations. Accordingly, a (thermal) dissipation added on the bending moment produces exponential stability if and only if the so called “equal wave speeds” condition is satisfied. This remarkable property extends to the case of non-homogeneous coefficients. In this paper, we consider a non-homogeneous thermoelastic system with dissipation restricted to the shear stress. To this new problem, by means of a delicate control observability analysis, we prove that a local version of the equal wave speeds condition is sufficient for the exponential stability of the system. Otherwise, we study the polynomial stability of the system with decay rate depending on the regularity of initial data.
PubDate: 2017-02-10
DOI: 10.1007/s00574-017-0030-3

• New Irreducible Components of the Space of Foliations Associated to the
Affine Lie Algebra
• Authors: Ruben Lizarbe
Abstract: We construct a family of irreducible components of space of holomorphic foliations of codimension one on $$\mathbb {P}^3$$ associated to some affine Lie algebra.
PubDate: 2017-01-31
DOI: 10.1007/s00574-017-0029-9

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