Invariant Measures of Non-Uniformly Expanding Maps with Higher Order Critical Set

TL;DR

This paper establishes the existence and uniqueness of absolutely continuous invariant measures for generalized Viana maps with higher order critical points, leading to super-polynomial decay of correlations.

Contribution

It introduces a new analysis for non-uniformly expanding maps with higher order critical points, extending previous results on invariant measures.

Findings

Existence and uniqueness of invariant measures

Super-polynomial decay of correlations

Generalization of Viana maps with higher order critical points

Abstract

We prove existence and uniqueness of absolutely continuous invariant measures for generalizations of Viana maps admitting a higher order critical point introduced in arXiv:2312.00906. As a consequence of our approach, we obtain super-polynomial decay of correlations.