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Equidistribution speed for endomorphisms of projective spaces

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Abstract

Let f be a non-invertible holomorphic endomorphism of \({\mathbb{P}^{k}}\), f n its iterate of order n and μ the equilibrium measure of f. We estimate the speed of convergence in the following known result. If a is a Zariski generic point in \({\mathbb{P}^{k}}\), the probability measures, equidistributed on the preimages of a under f n, converge to μ as n goes to infinity.

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Authors and Affiliations

  1. UPMC Univ Paris 06, UMR 7586, Institut de Mathématiques de Jussieu, 75005, Paris, France

    Tien-Cuong Dinh

  2. Université Paris-Sud, Mathématique-Bâtiment 425, 91405, Orsay, France

    Nessim Sibony

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  1. Tien-Cuong Dinh
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  2. Nessim Sibony
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Correspondence to Nessim Sibony.

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Dinh, TC., Sibony, N. Equidistribution speed for endomorphisms of projective spaces. Math. Ann. 347, 613–626 (2010). https://doi.org/10.1007/s00208-009-0445-2

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  • DOI: https://doi.org/10.1007/s00208-009-0445-2

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