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Mathematics > Dynamical Systems

arXiv:math/0401250 (math)
[Submitted on 20 Jan 2004]

Title:Linearisation d'endomorphismes holomorphes de CP(k) et caracterisation des exemples de Lattes par leur mesure de Green

Authors:Francois Berteloot, Christophe Dupont
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Abstract: Let f an holomorphic endomorphism of CP(k) with degree larger than 2. We show that if the Green measure of f is not singular, then f is rigid : it is a Lattes example. The proof relies on a linearization property of the iterates of f, along typical orbits. This property allow us to regularize the Green current, and to prove the rigidity. -- -- --
Soit f un endomorphisme holomorphe de CP(k) de degre plus grand que 2. Nous montrons que si la mesure de Green de f n'est pas singuliere, alors f est tres rigide : c'est un exemple de Lattes. La demonstration repose sur une propriete de linearisation des iteres de f le long d'orbites typiques. Cette propriete nous permet de "regulariser" le courant de Green, et d'en deduire la rigidite.
Comments: 19 pages, in french
Subjects: Dynamical Systems (math.DS); Complex Variables (math.CV)
MSC classes: 32H50, 37F
Cite as: arXiv:math/0401250 [math.DS]
  (or arXiv:math/0401250v1 [math.DS] for this version)
  https://doi.org/10.48550/arXiv.math/0401250

Submission history

From: Christophe Dupont [view email] [via CCSD proxy]
[v1] Tue, 20 Jan 2004 12:57:09 UTC (19 KB)
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