Large entropy measures for endomorphisms of CP(k)

2009/11/24 by Christophe Dupont, Dupont, Christophe
Computer Science · Engineering · Mathematics · #37C40 #37F10 #Artificial Immune Systems Applications #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #math.CV #math.DS #msc:37C40 #msc:37F10 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.0911.4675

24 pages

arxiv created 2009/11/24 · openalex publication_date 2009/11/24 · arxiv updated 2009/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f be an holomorphic endomorphism of ℂℙ^k. We construct by using coding techniques a class of ergodic measures as limits of non-uniform probability measures on preimages of points. We show that they have large metric entropy, close to log d^k. We establish for them strong stochastic properties and prove the positivity of their Lyapunov exponents. Since they have large entropy, those measures are supported in the support of the maximal entropy measure of f. They in particular provide lower bounds for the Hausdorff dimension of the Julia set.

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