Non uniformly hyperbolic diffeomorphisms derived from the standard map

TL;DR

This paper demonstrates that coupling the standard map with a fast hyperbolic system results in a robustly non-uniformly hyperbolic dynamical system, expanding understanding of complex chaotic behaviors.

Contribution

It introduces a novel method of deriving non-uniform hyperbolicity by coupling the standard map with hyperbolic systems, showing robustness of this property.

Findings

System is robustly non-uniformly hyperbolic

Coupling induces complex chaotic dynamics

Extends understanding of hyperbolic systems

Abstract

We prove that the system resulting of coupling the standard map with a fast hyperbolic system is robustly non-uniformly hyperbolic.