Ergodicity of Anosov Actions.
Ergodicity of harmonic invariant measures for the geodesic flow on hyperbolic spaces.
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
Estimation de l'entropie des systèmes lagrangiens sans points conjugués
Étude d’une transformation non uniformément hyperbolique de l’intervalle
Nous étudions un exemple de transformation non uniformément hyperbolique de l’intervalle . Des exemples analogues ont été étudiés par de nombreux auteurs. Notre méthode utilise une théorie spectrale, pour une classe d’opérateurs vérifiant des conditions faibles de Doeblin-Fortet, introduite dans [1]. Elle nous permet, en particulier, de donner une estimation de la vitesse de décroissance des corrélations pour des fonctions non höldériennes.
Eventually periodic points of infra-nil endomorphisms.
Exactness of expanding mappings
Exactness of skew products with expanding fibre maps
We give an elementary proof for the uniqueness of absolutely continuous invariant measures for expanding random dynamical systems and study their mixing properties.
Examples of Expanding Endomorphisms on Exotic Tori.
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.
Existence and multiplicity results for homoclinic orbits of Hamiltonian systems.
Existence of eigenvalues for (uaa) Markov maps.
Existence of non-uniform cocycles on uniquely ergodic systems
Existence of Periodic Points of Maps of S1.
Existence of pullback attractors for the coupled suspension bridge equations.
Existence of unique SRB-measures is typical for real unicritical polynomial families
Expanding attractors
Expanding maps on Cantor sets and analytic continuation of zeta functions
Expanding repellers in limit sets for iterations of holomorphic functions
We prove that for Ω being an immediate basin of attraction to an attracting fixed point for a rational mapping of the Riemann sphere, and for an ergodic invariant measure μ on the boundary FrΩ, with positive Lyapunov exponent, there is an invariant subset of FrΩ which is an expanding repeller of Hausdorff dimension arbitrarily close to the Hausdorff dimension of μ. We also prove generalizations and a geometric coding tree abstract version. The paper is a continuation of a paper in Fund. Math. 145...