MME for Mating Correspondences

2023/10/22 by Vanessa Matus de la Parra, De La Parra, Vanessa Matus · 1 citation
Computer Science · Mathematics · #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2310.14330

openalex publication_date 2023/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use the measure theoretical entropy from Vivas-Sirvent and the topological entropies from Dinh-Sibony and Kelly-Tennant to prove that the equidistribution measures μ_- and μ₊ found by the author maximize entropy for the 1-parameter family \lbraceF_a\rbrace_a studied by Bullett-Lomonaco. We find as well a measure of maximal entropy for the composition of two deleted covering correspondences studied by Bullett.

Cited by

• Uniqueness of the equilibrium state in the dynamics of holomorphic correspondences

Related

• The entropy of holomorphic correspondences: exact computations and\n rational semigroups
• Upper bound for topological entropy of a meromorphic correspondence
• Uniqueness and exponential mixing for the measure of maximal entropy for piecewise hyperbolic maps
• Weak approximation of an invariant measure and a low boundary of the entropy
• Information Measures for Entropy and Symmetry