• Corpus ID: 244130103

Entropy of irregular points that are not uniformly hyperbolic

  title={Entropy of irregular points that are not uniformly hyperbolic},
  author={Xiaobo Hou and Xueting Tian},
In this article we prove that for a C diffeomorphism on a compact Riemannian manifold, if there is a hyperbolic ergodic measure whose support is not uniformly hyperbolic, then the topological entropy of the set of irregular points that are not uniformly hyperbolic is larger than or equal to the metric entropy of the hyperbolic ergodic measure. In the process of proof, we give an abstract general mechanism to study topological entropy of irregular points provided that the system has a sequence… 



Strongly distributional chaos of irregular orbits that are not uniformly hyperbolic

In this article we prove that for a diffeomorphism on a compact Riemannian manifold, if there is a nontrival homoclinic class that is not uniformly hyperbolic or the diffeomorphism is a C and there

Maximal entropy measures for certain partially hyperbolic, derived from Anosov systems

Abstract We show that a class of robustly transitive diffeomorphisms originally described by Mañé are intrinsically ergodic. More precisely, we obtain an open set of diffeomorphisms which fail to be

The Entropy Conjecture for Diffeomorphisms away from Tangencies

We prove that every C1 diffeomorphism away from homoclinic tangencies is entropy expansive, with locally uniform expansivity constant. Consequently, such diffeomorphisms satisfy Shub's entropy

On the irregular points for systems with the shadowing property

We prove that when $f$ is a continuous self-map acting on a compact metric space $(X,d)$ that satisfies the shadowing property, then the set of irregular points (i.e., points with divergent Birkhoff

SRB measures for partially hyperbolic systems whose central direction is mostly contracting

We consider partially hyperbolic diffeomorphisms preserving a splitting of the tangent bundle into a strong-unstable subbundleEuu (uniformly expanding) and a subbundleEc, dominated byEuu.We prove

Topological entropy of level sets of empirical measures for non-uniformly expanding maps

In this article we obtain a variational principle for saturated sets for maps with some non-uniform specification properties. More precisely, we prove that the topological entropy of saturated sets

Sets of “Non-typical” points have full topological entropy and full Hausdorff dimension

For subshifts of finite type, conformal repellers, and conformal horseshoes, we prove that the set of points where the pointwise dimensions, local entropies, Lyapunov exponents, and Birkhoff averages

Entropy-Expansiveness and Domination for Surface Diffeomorphisms

Let f : M → M be a Cr-diffeomorphism, r ≥ 1, deffined on a closed manifold M. We prove that if M is a surface and K ⊂ M is a compact invariant set such that TKM = E ⊕ F is a dominated splitting then

Genericity of historic behavior for maps and flows

We establish a sufficient condition for a continuous map, acting on a compact metric space, to have a Baire residual set of points exhibiting historic behavior (also known as irregular points). This

Bernoulli Diffeomorphisms on surfaces

The smooth ergodic theory deals with the metric (ergodic) properties of classical dynamical systems (i.e., diffeomorphisms and smooth one-parameter flows on smooth manifolds) with respect to a