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arXiv · 2311.05577

Thermodynamic formalism for discontinuous maps and statistical properties of their equilibrium states

Rafael Bilbao·Rafael Lucena
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Abstract

In this article, we develop a functional-analytic framework to establish existence, uniqueness, regularity of disintegration, and statistical properties of equilibrium states for a broad class of dynamical systems, potentially discontinuous and not necessarily locally invertible. Our approach is applied to a family of piecewise partially hyperbolic maps and associated classes of potentials. We further prove several statistical limit theorems, including exponential decay of correlations, and propose related questions and conjectures. A collection of examples illustrating the applicability of our results is provided, including partially hyperbolic attractors over horseshoes, discontinuous systems, non-invertible dynamical systems admitting a semi-conjugacy to intermittent maps such as the Manneville--Pomeau map, and fat solenoidal attractors.

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Rafael Bilbao, Rafael Lucena. 2023-11-09. Thermodynamic formalism for discontinuous maps and statistical properties of their equilibrium states. https://doi.org/10.1016/j.chaos.2026.118019

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