Weak Gibbs measures as Gibbs measures for asymptotically additive sequences

TL;DR

This paper demonstrates that weak Gibbs measures for asymptotically additive sequences can be viewed as Gibbs measures for different such sequences, enabling new applications in multifractal analysis.

Contribution

It proves that weak Gibbs measures are equivalent to Gibbs measures for other asymptotically additive sequences, broadening their applicability.

Findings

Weak Gibbs measures can be represented as Gibbs measures for alternative sequences.

This equivalence allows applying dimension theory results to weak Gibbs measures.

Facilitates multifractal analysis for continuous potentials using asymptotically additive sequences.

Abstract

In this note we prove that every weak Gibbs measure for an asymptotically additive sequences is a Gibbs measure for another asymptotically additive sequence. In particular, a weak Gibbs measure for a continuous potential is a Gibbs measure for an asymptotically additive sequence. This allows, for example, to apply recent results on dimension theory of asymptotically additive sequences to study multifractal analysis for weak Gibbs measure for continuous potentials.