Entropy of meromorphic maps and dynamics of birational maps

2008/06/26 by Henry de Thélin, Henry De Thelin, De Thelin, Henry +2 · 1 citation
Mathematics · #32H04 #32Uxx #37A35 #37Dxx #37Fxx #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions #advanced mathematical theories #math.CV #math.DS #msc:32H04 #msc:32Uxx #msc:37A35 #msc:37Dxx #msc:37Fxx

paper · pdf · doi:10.48550/arxiv.0806.4284

107 pages

arxiv created 2008/06/26 · openalex publication_date 2008/06/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the dynamics of meromorphic maps for a compact Kaehler manifold X. More precisely, we give a simple criterion that allows us to produce a measure of maximal entropy. We can apply this result to bound the Lyapunov exponents. Then, we study the particular case of a family of generic birational maps of P^k for which we construct the Green currents and the equilibrium measure. We use for that the theory of super-potentials. We show that the measure is mixing and gives no mass to pluripolar sets. Using the criterion we get that the measure is of maximal entropy. It implies finally that the measure is hyperbolic.

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