Separatrices for non solvable dynamics on ℂ , 0

Isao Nakai

Annales de l'institut Fourier (1994)

  • Volume: 44, Issue: 2, page 569-599
  • ISSN: 0373-0956

Abstract

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We define the separatrices for pseudogroups of diffeomorphisms of open neighbourhoods of the origin in the complex plane ℂ and prove their existence for non solvable pseudogroups (Theorem 1). This extends a result by Shcherbakov (in [21]) accurately. Our method also applies to prove the topological rigidity theorem for generic pseudogroups attributed to Shcherbakov (dans [20]).

How to cite

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Nakai, Isao. "Separatrices for non solvable dynamics on ${\mathbb {C}},0$." Annales de l'institut Fourier 44.2 (1994): 569-599. <http://eudml.org/doc/75074>.

@article{Nakai1994,
abstract = {We define the separatrices for pseudogroups of diffeomorphisms of open neighbourhoods of the origin in the complex plane $\{\Bbb C\}$ and prove their existence for non solvable pseudogroups (Theorem 1). This extends a result by Shcherbakov (in [21]) accurately. Our method also applies to prove the topological rigidity theorem for generic pseudogroups attributed to Shcherbakov (dans [20]).},
author = {Nakai, Isao},
journal = {Annales de l'institut Fourier},
keywords = {separatrices for pseudogroups of diffeomorphisms of open neighbourhoods of the origin in the complex plane; non solvable pseudogroups; topological rigidity theorem for generic pseudogroups},
language = {eng},
number = {2},
pages = {569-599},
publisher = {Association des Annales de l'Institut Fourier},
title = {Separatrices for non solvable dynamics on $\{\mathbb \{C\}\},0$},
url = {http://eudml.org/doc/75074},
volume = {44},
year = {1994},
}

TY - JOUR
AU - Nakai, Isao
TI - Separatrices for non solvable dynamics on ${\mathbb {C}},0$
JO - Annales de l'institut Fourier
PY - 1994
PB - Association des Annales de l'Institut Fourier
VL - 44
IS - 2
SP - 569
EP - 599
AB - We define the separatrices for pseudogroups of diffeomorphisms of open neighbourhoods of the origin in the complex plane ${\Bbb C}$ and prove their existence for non solvable pseudogroups (Theorem 1). This extends a result by Shcherbakov (in [21]) accurately. Our method also applies to prove the topological rigidity theorem for generic pseudogroups attributed to Shcherbakov (dans [20]).
LA - eng
KW - separatrices for pseudogroups of diffeomorphisms of open neighbourhoods of the origin in the complex plane; non solvable pseudogroups; topological rigidity theorem for generic pseudogroups
UR - http://eudml.org/doc/75074
ER -

References

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Citations in EuDML Documents

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  1. Michel Belliart, Sur certains pseudogroupes de biholomorphismes locaux de ( ℂ n , 0 )
  2. Isao Nakai, The classification of curvilinear angles in the complex plane and the groups of ± holomorphic diffeomorphisms
  3. Julio C. Rebelo, Ergodicity and rigidity for certain subgroups of Diff ω ( S 1 )
  4. Yoshifumi Matsuda, Groups of real analytic diffeomorphisms of the circle with a finite image under the rotation number function
  5. A. Lins Neto, P. Sad, B. Scárdua, On topological rigidity of projective foliations

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