Dynamics of multi-resonant biholomorphisms
Complex Variables
2012-07-20 v3 Dynamical Systems
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.
Cite
@article{arxiv.1106.1962,
title = {Dynamics of multi-resonant biholomorphisms},
author = {Filippo Bracci and Jasmin Raissy and Dmitri Zaitsev},
journal= {arXiv preprint arXiv:1106.1962},
year = {2012}
}
Comments
Final version, accepted in International Mathematics Research Notices