Decay of correlations for invertible systems with non-H\"older observables

TL;DR

This paper investigates how correlations decay in invertible hyperbolic dynamical systems, providing upper bounds based on the observables' modulus of continuity, with applications to Hénon and Solenoid maps exhibiting intermittency.

Contribution

It offers new upper estimates for correlation decay in systems with non-Hölder observables, extending understanding beyond classical regularity assumptions.

Findings

Correlation decay rates depend on the modulus of continuity of observables.

Results apply to Hénon maps with intermittency.

Results extend to Solenoid maps with intermittency.

Abstract

An invertible dynamical system with some hyperbolic structure is considered. Upper estimates for the correlations of continuous observables is given in terms of modulus of continuity. The result is applied to certain H\'enon maps and Solenoid maps with intermittency.