Twisted recurrence for dynamical systems with exponential decay of correlations

TL;DR

This paper investigates the recurrence behavior of points in dynamical systems with exponential decay of correlations, establishing a generalized quantitative recurrence result under Lipschitz transformations.

Contribution

It introduces a new recurrence theorem for systems with exponential decay of correlations, incorporating Lipschitz twists, extending previous results in dynamical systems theory.

Findings

Proves a generalized recurrence result under decay of correlations.

Establishes quantitative recurrence estimates with Lipschitz twists.

Demonstrates applicability to systems with exponential decay of correlations.

Abstract

We study the set of points returning infinitely often to a sequence of targets dependent on the starting points. With an assumption of decay of correlations for L1 against bounded variations, we prove a generalized quantitative recurrence result under Lipschitz twists.