Multifractal analysis for expanding interval maps with infinitely many branches

TL;DR

This paper extends multifractal analysis to expanding interval maps with infinitely many branches, revealing significant differences from the finite-branch case, and broadening understanding of complex dynamical systems.

Contribution

It generalizes previous multifractal analysis from finitely to infinitely many branches, highlighting key differences and advancing the theoretical framework.

Findings

Identifies substantial differences between finite and infinite branch cases.

Develops a multifractal decomposition framework for infinite-branch maps.

Enhances understanding of dynamical complexity in systems with infinitely many branches.

Abstract

In this paper we investigate multifractal decompositions based on values of Birkhoff averages of functions from a class of symbolically continuous functions. This will be done for an expanding interval map with infinitely many branches and is a generalisation of previous work for expanding maps with finitely many branches. We show that there are substantial differences between this case and the setting where the expanding map has only finitely many branches.