Geometric normalization
Dynamical Systems
2025-06-16 v1
Abstract
For a local analytic diffeomorphism of the plane with an irrational elliptic fixed point at 0, we introduce the notion of ``geometric normalization'', which includes the classical formal normalizations as a special case: it is a formal conjugacy to a formal diffeomorphism which preserves the foliation by circles centered at 0. We show that geometric normalizations, despite of non-uniqueness, correspond in a natural way to a unique formal invariant foliation. We show, in various contexts, generic results of divergence for the geometric normalizations, which amount to the generic non-existence of any analytic invariant foliation.
Cite
@article{arxiv.2506.11580,
title = {Geometric normalization},
author = {Alain Chenciner and David Sauzin and Qiaoling Wei},
journal= {arXiv preprint arXiv:2506.11580},
year = {2025}
}