A variational principle for systems with nonuniformly hyperbolic behavior with applications to the dimension theory

2015/08/06 by Fernando José Sánchez-Salas, Sánchez-Salas, Fernando José
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #37D25 #37D35 #Caveolin-1 and cellular processes #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Protein Tyrosine Phosphatases #Quantum chaos and dynamical systems #math.DS #msc:37D25 #msc:37D35

paper · pdf · doi:10.48550/arxiv.1508.01320

arxiv created 2015/08/06 · openalex publication_date 2015/08/06 · arxiv updated 2015/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f be a C^1+α nonuniformly hyperbolic diffeomorphism. We use a a nonadditive version of the topological pressure of a class of admissible, possibly noncontinuous potentials P^*(Φ) to prove the following variational equation: P^*(Φ) = sup_Ω∈ \mathcal HP^*(f|Ω,Φ) supremum taken over the set \mathcal H of basic subsets in M. As a consequence we find a lower bound for the Cantor dimension of the stable and unstable Cantor sets of a non trivial conformal nonuniformly hyperbolic isolated sets.

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