The goal of this paper is to study the dynamics of holomorphic diffeomorphisms in such that the resonances among the first 1≤r≤n eigenvalues of the differential are generated over by a finite number of-linearly independent multi-indices (and more resonances are allowed for other eigenvalues). We give sharp conditions for the existence of basins of attraction where a Fatou coordinate can be defined. Furthermore, we obtain a generalization of the Leau-Fatou flower theorem, providing a complete description of the dynamics in a full neighborhood of the origin for 1-resonant parabolically attracting holomorphic germs in Poincaré-Dulac normal form.
Bracci, F., Raissy, J., Zaitsev, D. (2013). Dynamics of multi-resonant biholomorphisms. INTERNATIONAL MATHEMATICS RESEARCH NOTICES(20), 4772-4797 [DOI: 10.1093/imrn/rns192].
Dynamics of multi-resonant biholomorphisms
BRACCI, FILIPPO;
2013-01-01
Abstract
The goal of this paper is to study the dynamics of holomorphic diffeomorphisms in such that the resonances among the first 1≤r≤n eigenvalues of the differential are generated over by a finite number of-linearly independent multi-indices (and more resonances are allowed for other eigenvalues). We give sharp conditions for the existence of basins of attraction where a Fatou coordinate can be defined. Furthermore, we obtain a generalization of the Leau-Fatou flower theorem, providing a complete description of the dynamics in a full neighborhood of the origin for 1-resonant parabolically attracting holomorphic germs in Poincaré-Dulac normal form.File | Dimensione | Formato | |
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