The entropy of holomorphic correspondences: exact computations and\n rational semigroups

2020/04/28 by Gautam Bharali, Bharali, Gautam, Shrihari Sridharan +1 · 1 citation
Mathematics · #30D05 #37B40 #37F05 (Primary) 32H50 (Secondary) #Advanced Topology and Set Theory #Analytic and geometric function theory #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2004.13691

openalex publication_date 2020/04/28 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We study two notions of topological entropy of correspondences introduced by\nFriedland and Dinh-Sibony. Upper bounds are known for both. We identify a class\nof holomorphic correspondences whose entropy in the sense of Dinh-Sibony equals\nthe known upper bound. This provides an exact computation of the entropy for\nrational semigroups. We also explore a connection between these two notions of\nentropy.\n

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

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