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Hauptverfasser: Chenciner, Alain, Sauzin, David, Wei, Qiaoling
Format: Preprint
Veröffentlicht: 2025
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Online-Zugang:https://arxiv.org/abs/2506.11580
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author Chenciner, Alain
Sauzin, David
Wei, Qiaoling
author_facet Chenciner, Alain
Sauzin, David
Wei, Qiaoling
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2506_11580
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Geometric normalization
Chenciner, Alain
Sauzin, David
Wei, Qiaoling
Dynamical Systems
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.
title Geometric normalization
topic Dynamical Systems
url https://arxiv.org/abs/2506.11580