The Historic Set of Ergodic Averages in Some Nonuniformly Hyperbolic Systems

TL;DR

This paper investigates the properties of historic sets of ergodic averages in certain nonuniformly hyperbolic systems, including multidimensional nonuniformly expanding maps and Viana maps, revealing new dynamical behaviors.

Contribution

It provides new insights into the structure of historic sets in nonuniformly hyperbolic systems, extending previous results to broader classes like Viana maps.

Findings

Analysis of the size and complexity of historic sets

Extension of ergodic average properties to multidimensional systems

Identification of conditions under which historic behavior occurs

Abstract

This article is devoted to the study of the historic set 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.