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.
 Publication:

arXiv eprints
 Pub Date:
 November 2021
 arXiv:
 arXiv:2111.08325
 Bibcode:
 2021arXiv211108325H
 Keywords:

 Mathematics  Dynamical Systems
 EPrint:
 24 pages. arXiv admin note: substantial text overlap with arXiv:2111.06055