Repellers for non-uniformly expanding maps with singular or critical points

TL;DR

This paper investigates how non-uniformly expanding maps with singular or critical points can be approximated by uniformly expanding repellers, enhancing understanding of their dynamical quantifiers.

Contribution

It introduces a method to approximate dynamical quantifiers of non-uniformly expanding maps with repellers, even with singular or critical points, extending previous uniform expansion results.

Findings

Dynamical quantifiers can be approximated by uniformly expanding repellers.

The approach applies to maps with critical or singular points outside a smooth region.

Provides a framework for analyzing non-uniformly expanding systems with singularities.

Abstract

Given an ergodic measure with positive entropy and only positive Lyapunov exponents, its dynamical quantifiers can be approximated by means of quantifiers of some family of uniformly expanding repellers. Here non-uniformly expanding maps are studied that are $C^{1+\beta}$ smooth outside a set of possibly critical or singular points.