Thermodynamic formalism for Lorenz maps

2012/09/10 by Renaud Leplaideur, Leplaideur, Renaud, Vilton Pinheiro +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Nonlinear Dynamics and Pattern Formation

paper · pdf · doi:10.48550/arxiv.1209.2008

openalex publication_date 2012/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a 2-dimensional map representing an expanding geometric Lorenz at- tractor we prove that the attractor is the closure of a union of as long as possible unstable leaves with ending points. This allows to define the notion of good measures, those giving full measure to the union of these open leaves. Then, for any Hölder continuous potential we prove that there exists at most one relative equilibrium state among the set of good measures. Condition yielding existence are given.

Citations

• Local product structure for Equilibrium States

Cited by

• Uniqueness of the measure of maximal entropy for singular hyperbolic flows in dimension 3 and more results on equilibrium states

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