Ergodic properties of Viana-like maps with singularities in the base dynamics

TL;DR

This paper studies Viana-like maps with singular base dynamics, establishing the existence of unique invariant measures and demonstrating stretched exponential decay of correlations and large deviations.

Contribution

It introduces new results on ergodic properties of Viana maps with singularities, including existence of unique invariant measures and decay rates.

Findings

Existence of a unique absolutely continuous invariant measure

Stretched exponential decay of correlations

Stretched exponential large deviations

Abstract

We consider two examples of Viana maps for which the base dynamics has singularities (discontinuities or critical points) and show the existence of a unique absolutely continuous invariant probability measure and related ergodic properties such as stretched exponential decay of correlations and stretched exponential large deviations.