Multifractal analysis of non-uniformly hyperbolic systems

TL;DR

This paper establishes a multifractal formalism for Birkhoff averages in certain non-uniformly hyperbolic systems, including the Manneville--Pomeau map, advancing understanding of their complex statistical properties.

Contribution

It introduces a multifractal analysis framework applicable to non-uniformly hyperbolic maps, extending previous theories to new classes of dynamical systems.

Findings

Proved a multifractal formalism for Birkhoff averages in non-uniformly hyperbolic maps.

Included analysis of the Manneville--Pomeau map as a key example.

Enhanced understanding of the statistical complexity of non-uniformly hyperbolic systems.

Abstract

We prove a multifractal formalism for Birkhoff averages of continuous functions in the case of some non-uniformly hyperbolic maps, which includes interval examples such as the Manneville--Pomeau map.