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Chapitre D'ouvrage Asterisque Année : 2020

Smooth Siegel disks everywhere

Résumé

We prove the existence of Siegel disks with smooth boundaries in most families of holomorphic maps fixing the origin. The method can also yield other types of regularity conditions for the boundary. The family is required to have an indifferent fixed point at 0, to be parameterized by the rotation number α, to depend on α in a Lipschitz-continuous way, and to be non-degenerate. A degenerate family is one for which the set of non-linearizable maps is not dense. We give a characterization of degenerate families, which proves that they are quite exceptional.
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Dates et versions

hal-03133802 , version 1 (07-02-2021)

Identifiants

Citer

Artur Avila, Xavier Buff, Arnaud Chéritat. Smooth Siegel disks everywhere. Some aspects of the theory of dynamical systems: a tribute to Jean-Christophe Yoccoz, Volume II, 416, pp.133-180, 2020, Astérisque, 978-2-85629-917-3. ⟨10.24033/ast.1112⟩. ⟨hal-03133802⟩
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