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arXiv · 1106.1962

Dynamics of multi-resonant biholomorphisms

Filippo Bracci·Jasmin Raissy·Dmitri Zaitsev
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Abstract

The goal of this paper is to study the dynamics of holomorphic diffeomorphisms in C^n such that the resonances among the first 1<= r<= n eigenvalues of the differential are generated over N by a finite number of Q-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 Poincare'-Dulac normal form.

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Filippo Bracci, Jasmin Raissy, Dmitri Zaitsev. 2012-07-19. Dynamics of multi-resonant biholomorphisms. https://arxiv.org/abs/1106.1962

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