Dynamics of one-resonant biholomorphisms
Complex Variables
2015-02-16 v2 Dynamical Systems
Abstract
Our first main result is a construction of a simple formal normal form for holomorphic diffeomorphisms in C^n whose differentials have one-dimensional family of resonances in the first m eigenvalues, m <= n (but more resonances are allowed for other eigenvalues). Next, we provide invariants and give conditions for the existence of basins of attraction. Finally, we give applications and examples demonstrating the sharpness of our conditions.
Cite
@article{arxiv.0912.0428,
title = {Dynamics of one-resonant biholomorphisms},
author = {Filippo Bracci and Dmitri Zaitsev},
journal= {arXiv preprint arXiv:0912.0428},
year = {2015}
}
Comments
Final version, to appear in The Journal of the European Mathematical Society (JEMS)