Smooth Siegel disks everywhere [ Back ]

Date:
20.10.20   
Times:
16:30 to 17:30
Place:
on-line
Speaker:
Arnaud Chéritat
University:
Institut de Mathématiques de Toulouse

Abstract

 

Joint work with Artur Ávila and Xavier Buff. 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.