Multifractal analysis in non-uniformly hyperbolic interval maps

TL;DR

This paper investigates the Hausdorff dimension of specific level sets in non-uniformly hyperbolic interval maps, enhancing understanding of their fractal geometry under ergodic measures.

Contribution

It introduces a method to analyze the Hausdorff dimension of intrinsic level sets in non-uniformly hyperbolic maps with finitely many branches.

Findings

Determined the Hausdorff dimension for a class of level sets.

Extended multifractal analysis to non-uniformly hyperbolic systems.

Provided new insights into the geometric structure of these maps.

Abstract

In this paper, we study the Hausdorff dimension of the generalized intrinsic level set with respect to the given ergodic meausre in a class of non-uniformly hyperbolic interval maps with finitely many branches.