Modulus of analytic classification for unfoldings of resonant diffeomorphisms
Dynamical Systems
2017-02-10 v1
Abstract
We provide a complete system of analytic invariants for unfoldings of non-linearizable resonant complex analytic diffeomorphisms as well as its geometrical interpretation. In order to fulfill this goal we develop an extension of the Fatou coordinates with controlled asymptotic behavior in the neighborhood of the fixed points. The classical constructions are based on finding regions where the dynamics of the unfolding is topologically stable. We introduce a concept of infinitesimal stability leading to Fatou coordinates reflecting more faithfully the analytic nature of the unfolding. These improvements allow us to control the domain of definition of a conjugating mapping and its power series expansion.
Keywords
Cite
@article{arxiv.math/0608545,
title = {Modulus of analytic classification for unfoldings of resonant diffeomorphisms},
author = {Javier Ribon},
journal= {arXiv preprint arXiv:math/0608545},
year = {2017}
}
Comments
55 pages