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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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

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

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

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

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

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

Authors:Adel Chala 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

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

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