Separatrices for non solvable dynamics on \(\mathbb{C},0\)
type: Item
instance of: scholarly article
title: Separatrices for non solvable dynamics on \(\mathbb{C},0\)
zbMATH Open document ID: 0804.57022
author: Isao Nakai
publication date: 1995-01-24T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/75074
review text: We define the separatrices for pseudogroups of diffeomorphisms of open neighbourhoods of the origin in the complex plane \(\mathbb{C}\) and prove their existence for non solvable pseudogroups (Theorem 1). This extends a result by \textit{A. A. Shcherbakov} [Mosc. Univ. Math. Bull. 37, No. 4, 10- 16 (1982); translation from Vestn. Mosk. Univ., Ser. I 1982, No. 4, 10-15 (1982; Zbl 0517.30009)] accurately. Our method also applies to prove the topological rigidity theorem for generic pseudogroups attributed to Shcherbakov [Tr. Semin. Im. I. G. Petrovskogo 10, 170-196 (1984; Zbl 0568.30010)].
Mathematics Subject Classification ID: 57S99
Mathematics Subject Classification ID: 58H05
Mathematics Subject Classification ID: 37-XX
zbMATH DE Number: 672153
zbMATH Keywords: separatrices for pseudogroups of diffeomorphisms of open neighbourhoods of the origin in the complex plane
zbMATH Keywords: non solvable pseudogroups
zbMATH Keywords: topological rigidity theorem for generic pseudogroups
MaRDI profile type: Publication
OpenAlex ID: W2314603967
cites work: Fractional iteration near a fixpoint of multiplier 1.
cites work: Q4002072
cites work: Q5179742
cites work: Q3050699
cites work: Groupes d'automorphismes de $({\bbfC},0)$ et équations différentielles $ydy+\cdots =0$
cites work: Problèmes de modules pour les formes différentielles singulières dans le plan complexe. (Moduli problems for singular differential forms in the complex plane)
cites work: The transverse dynamics of a holomorphic flow
cites work: Q3208965
cites work: Q3715461
cites work: Q4002482
cites work: Q5647151
cites work: Versal deformations of differential forms of degree \(\alpha\) on a line
cites work: Holonomie et intégrales premières
cites work: Q3802291
cites work: On topological types of polynomial mappings
cites work: Topology of complex webs of codimension one and geometry of projective space curves
cites work: Construction of singular holomorphic vector fields and foliations in dimension two
cites work: Q3684361
cites work: On the density of an orbit of a pseudogroup of conformal mappings and a generalization of the Khudaj-Verenov theorem
cites work: Analytic classification of germs of conformal mappings \((C,O) \to (C,O)\) with identity linear part
cites work: Analytic classification of pairs of involutions and its applications
cites work: Q3847130
DOI: 10.5802/AIF.1410
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 672153