ﻻ يوجد ملخص باللغة العربية
In this work we give general conditions under which a $C^0$ perturbation of an expansive homeomorphim with specification property has an unique Bowen measure, that is, there is an ergodic probability measure which is the unique measure maximizing the topological entropy. We apply these conditions to show that several derived from Anosov diffeomorphims have a unique Bowen measure.
Given a general Anosov abelian action on a closed manifold, we study properties of certain invariant measures that have recently been introduced in cite{BGHW20} using the theory of Ruelle-Taylor resonances. We show that these measures share many prop
We prove that for Anosov maps of the $3$-torus if the Lyapunov exponents of absolutely continuous measures in every direction are equal to the geometric growth of the invariant foliations then $f$ is $C^1$ conjugated to his linear part.
A {em sectional-Anosov flow} is a vector field on a compact manifold inwardly transverse to the boundary such that the maximal invariant set is sectional-hyperbolic (in the sense of cite{mm}). We prove that any $C^2$ transitive sectional-Anosov flow
We define for $mathbb{R}^kappa$-Anosov actions a notion of joint Ruelle resonance spectrum by using the techniques of anisotropic Sobolev spaces in the cohomological setting of joint Taylor spectra. We prove that these Ruelle-Taylor resonances are in
We prove that in an open and dense set, Symplectic linear cocycles over time one maps of Anosov flows, have positive Lyapunov exponents for SRB measures.