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Article Dans Une Revue Ergodic Theory and Dynamical Systems Année : 2020

DYNAMICS OF POST-CRITICALLY FINITE MAPS IN HIGHER DIMENSION

Résumé

We study the dynamics of post-critically finite endomorphisms of P^k(C). We prove that post-critically finite endomorphisms are always post-critically finite all the way down under a mild regularity condition on the post-critical set. We study the eigenvalues of periodic points of post-critically finite endomorphisms. Then, under a weak transversality condition and assuming Kobayashi hyperbolicity of the complement of the post-critical set, we prove that the only possible Fatou components are super-attracting basins, thus partially extending to any dimension a result of Fornaess-Sibony and Rong holding in the case k = 2.

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Dates et versions

hal-01362326 , version 1 (08-09-2016)

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Matthieu Astorg. DYNAMICS OF POST-CRITICALLY FINITE MAPS IN HIGHER DIMENSION. Ergodic Theory and Dynamical Systems, 2020, 40 (2), pp.289-308. ⟨10.1017/etds.2018.32⟩. ⟨hal-01362326⟩
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