Entropy of irregular points that are not uniformly hyperbolic

Abstract

In this article we prove that for a $C^{1+\alpha }$ 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 of nondecreasing invariant compact subsets such that every subsystem has shadowing property and is transitive.

24 pages. arXiv admin note: substantial text overlap with arXiv:2111.06055

References in corpus (2)

• Ergodic Average Of Typical Orbits And Typical Functions
• Strongly distributional chaos of irregular orbits that are not uniformly hyperbolic