Multifractal Analysis of Ergodic Averages in Some Nonuniformly Hyperbolic Systems

TL;DR

This paper investigates the multifractal properties of ergodic averages within certain nonuniformly hyperbolic systems, including multidimensional expanding maps and Viana maps, revealing complex fractal structures in their statistical behavior.

Contribution

It provides new multifractal analysis results for nonuniformly hyperbolic systems, extending understanding to multidimensional and Viana map classes.

Findings

Multifractal spectra characterized for specific nonuniformly hyperbolic systems.

Results applicable to robust classes of multidimensional expanding maps.

Enhanced understanding of ergodic averages in complex dynamical systems.

Abstract

This article is devoted to the study of the multifractal analysis of ergodic averages in some nonuniformly hyperbolic systems. In particular, our results hold for the robust classes of multidimensional nonuniformly expanding local diffeomorphisms and Viana maps.