Generic Points in Some Nonuniformly Hyperbolic Systems Via Pesin Theory

TL;DR

This paper investigates the topological pressure of generic points in nonuniformly hyperbolic systems using Pesin theory, with applications to certain diffeomorphisms including those derived from Anosov systems.

Contribution

It extends Pesin theory to analyze generic points' topological pressure in nonuniformly hyperbolic systems, including new classes of diffeomorphisms.

Findings

Topological pressure results for generic points in nonuniformly hyperbolic systems

Application of Pesin theory to specific classes of diffeomorphisms

Extension of existing theories to systems derived from Anosov systems

Abstract

This article is devoted to the investigation of the topological pressure of generic points for nonuniformly hyperbolic systems via Pesin theory. In particular, our result can be applied to the nonuniformly hyperbolic diffeomorphisms described by Katok and several other classes of diffeomorphisms derived from Anosov systems.