Constructing equilibrium states for Smale spaces

2024/03/07 by Parmenter, David, Pollicott, Mark · 2 citations
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2403.04646

Abstract

There are several known constructions of equilibrium states for Hölder continuous potentials in the context of both subshifts of finite type and uniformly hyperbolic systems. In this article we present another method of building such measures, formulated in the unified and more general setting of Smale spaces. This simultaneously extends the authors' previous work for hyperbolic attractors (modelled after Sinai's classical approach for SRB-measures) and gives a new and original construction of equilibrium states for subshifts of finite type.

Cited by

• Construction of equilibrium states revisited
• Local large deviation principle for Smale spaces

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