seminar: Dynamics of multi-resonant biholomorphisms
speaker: Jasmin Raissy (Universite' de Bordeaux)abstract: Normal forms are a very important tool in several branches of mathematics. I shall discuss the normalization and the linearization problems for germs of biholomorphism of several complex variables with an isolated fixed point, starting from the classical Poincare'-Dulac procedure, and then focusing on the case of multi-resonant biholomorphisms, i.e., such that the resonances among the eigenvalues of the differential are generated over N by a finite number of linearly independent multi-indices. I shall give sharp conditions for the existence of basins of attraction where a Fatou coordinate can be defined. Furthermore, we shall obtain a generalization of the Leau-Fatou flower theorem, providing a complete description of the dynamics in a full neighborhood of the fixed point for 1-resonant parabolically attracting holomorphic germs in Poincaré-Dulac normal form. (Joint work with Filippo Bracci and Dmitri Zaitsev).
timetable:
Thu 1 Mar, 16:00 - 17:00, Sala Conferenze Centro De Giorgi
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