We define the separatrices for pseudogroups of diffeomorphisms of open neighbourhoods of the origin in the complex plane 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]).
Nous définissons les séparatrices pour les pseudo-groupes de difféomorphismes de voisinages ouverts de l’origine du plan complexe , et nous démontrons leur existence pour les pseudo-groupes non résolubles (Théorème 1). Ceci précise un résultat de Shcherbakov (dans [21]). Notre méthode permet aussi de démontrer le théorème de rigidité topologique pour les pseudo-groupes génériques attribué à Shcherbakov (dans [20]).
@article{AIF_1994__44_2_569_0, author = {Nakai, Isao}, title = {Separatrices for non solvable dynamics on ${\mathbb {C}},0$}, journal = {Annales de l'Institut Fourier}, pages = {569--599}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {44}, number = {2}, year = {1994}, doi = {10.5802/aif.1410}, mrnumber = {95j:58124}, zbl = {0804.57022}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.1410/} }
TY - JOUR AU - Nakai, Isao TI - Separatrices for non solvable dynamics on ${\mathbb {C}},0$ JO - Annales de l'Institut Fourier PY - 1994 SP - 569 EP - 599 VL - 44 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.1410/ DO - 10.5802/aif.1410 LA - en ID - AIF_1994__44_2_569_0 ER -
%0 Journal Article %A Nakai, Isao %T Separatrices for non solvable dynamics on ${\mathbb {C}},0$ %J Annales de l'Institut Fourier %D 1994 %P 569-599 %V 44 %N 2 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.1410/ %R 10.5802/aif.1410 %G en %F AIF_1994__44_2_569_0
Nakai, Isao. Separatrices for non solvable dynamics on ${\mathbb {C}},0$. Annales de l'Institut Fourier, Volume 44 (1994) no. 2, pp. 569-599. doi : 10.5802/aif.1410. http://archive.numdam.org/articles/10.5802/aif.1410/
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