Ergodicity of some classes of meromorphic functions.
Erratum to "Minimal sets of non-resonant torus homeomorphisms" (Fund. Math. 211 (2011), 41-76)
Erratum to "Multifractal spectra of Birkhoff averages for a piecewise monotone interval map" (Fund. Math. 208 (2010), 95-121)
Essential dynamics for Lorenz maps on the real line and the lexicographical world
Estimates of topological entropy of continuous maps with applications.
Euclidean Mahler measure and twisted links.
Eventually cyclic spectra of parameterized flows.
Examples of minimal diffeomorphisms on 𝕋² semiconjugate to an ergodic translation
We prove that for every ϵ > 0 there exists a minimal diffeomorphism f: ² → ² of class and semiconjugate to an ergodic translation with the following properties: zero entropy, sensitivity to initial conditions, and Li-Yorke chaos. These examples are obtained through the holonomy of the unstable foliation of Mañé’s example of a derived-from-Anosov diffeomorphism on ³.
Exemples de classes d'automates cellulaires
Lorsqu'on observe des orbites de certains automates cellulaires, on peut penser qu'elles apparaissent comme des mélanges d'orbites d'autres automates (composants). Dans cet article, nous tentons de comprendre ce phénomène en construisant un hybride de deux automates au moyen d'un troisième. Deux types d'automates cellulaires sont introduits : les captifs et les foulards. Nous comparons des propriétés de ces hybrides dans le cadre des classifications algébriques introduites par [B. Martin...
Existence, blow-up and exponential decay for a nonlinear Love equation associated with Dirichlet conditions
In this paper we consider a nonlinear Love equation associated with Dirichlet conditions. First, under suitable conditions, the existence of a unique local weak solution is proved. Next, a blow up result for solutions with negative initial energy is also established. Finally, a sufficient condition guaranteeing the global existence and exponential decay of weak solutions is given. The proofs are based on the linearization method, the Galerkin method associated with a priori estimates, weak convergence,...
Existence criterions for generalized solutions of functional boundary value problems without growth restrictions
Existence of quadratic Hubbard trees
A (quadratic) Hubbard tree is an invariant tree connecting the critical orbit within the Julia set of a postcritically finite (quadratic) polynomial. It is easy to read off the kneading sequences from a quadratic Hubbard tree; the result in this paper handles the converse direction. Not every sequence on two symbols is realized as the kneading sequence of a real or complex quadratic polynomial. Milnor and Thurston classified all real-admissible sequences, and we give a classification of all complex-admissible...
Existence, uniqueness and global asymptotic stability for a class of complex-valued neutral-type neural networks with time delays
This paper explores the problem of delay-independent and delay-dependent stability for a class of complex-valued neutral-type neural networks with time delays. Aiming at the neutral-type neural networks, an appropriate function is constructed to derive the existence of equilibrium point. On the basis of homeomorphism theory, Lyapunov functional method and linear matrix inequality techniques, several LMI-based sufficient conditions on the existence, uniqueness and global asymptotic stability of equilibrium...
Expanding maps on Cantor sets and analytic continuation of zeta functions
Explicit computations of all finite index bimodules for a family of II factors
We study II factors and associated with good generalized Bernoulli actions of groups having an infinite almost normal subgroup with the relative property (T). We prove the following rigidity result : every finite index --bimodule (in particular, every isomorphism between and ) is described by a commensurability of the groups involved and a commensurability of their actions. The fusion algebra of finite index --bimodules is identified with an extended Hecke fusion algebra, providing the...
Extreme Relations for Topological Flows
We introduce the concept of an extreme relation for a topological flow as an analogue of the extreme measurable partition for a measure-preserving transformation considered by Rokhlin and Sinai, and we show that every topological flow has such a relation for any invariant measure. From this result, it follows, among other things, that any deterministic flow has zero topological entropy and any flow which is a K-system with respect to an invariant measure with full support is a topological K-flow....