Correlation decay and large deviations for mixed systems

TL;DR

This paper explores how low-dimensional dynamical systems with mixed phase space exhibit slow polynomial decay of correlations, linking this behavior to large deviations properties.

Contribution

It highlights the relationship between correlation decay rates and large deviations in mixed dynamical systems, providing insights into their statistical behavior.

Findings

Polynomial decay of correlations in mixed systems

Connection between decay rates and large deviations

Insights into statistical properties of low-dimensional systems

Abstract

We consider low--dimensional dynamical systems with a mixed phase space and discuss the typical appearance of slow, polynomial decay of correlations: in particular we emphasize how this mixing rate is related to large deviations properties.