Let be a -action on an orientable -dimensional manifold. Assume has an isolated compact orbit and let be a small tubular neighborhood of it. By a change of variables, we can write and , where is some interval containing 0.
In this work, we show that by a change of variables, outside , we can make invariant by transformations of the type , where and . As a corollary one cas describe completely the dynamics of in .
Soit une -action sur une variété orientable de dimension . Supposons que possède une orbite compacte isolée et soit un petit voisinage tubulaire de . À l’aide d’un changement de variables , nous pouvons écrire et , où est un intervalle réel contenant 0.
Dans ce travail nous montrons que par un changement de variables , qui est au-dehors de , nous pouvons rendre invariante par les transformations du type , où et . Comme corollaire nous pouvons décrire complètement la dynamique de sur .
@article{AIF_1994__44_5_1435_0, author = {Craizer, Marcos}, title = {Homogenization of codimension 1 actions of ${\mathbb {R}}^n$ near a compact orbit}, journal = {Annales de l'Institut Fourier}, pages = {1435--1448}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {44}, number = {5}, year = {1994}, doi = {10.5802/aif.1440}, mrnumber = {95m:58100}, zbl = {0820.34021}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.1440/} }
TY - JOUR AU - Craizer, Marcos TI - Homogenization of codimension 1 actions of ${\mathbb {R}}^n$ near a compact orbit JO - Annales de l'Institut Fourier PY - 1994 SP - 1435 EP - 1448 VL - 44 IS - 5 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.1440/ DO - 10.5802/aif.1440 LA - en ID - AIF_1994__44_5_1435_0 ER -
%0 Journal Article %A Craizer, Marcos %T Homogenization of codimension 1 actions of ${\mathbb {R}}^n$ near a compact orbit %J Annales de l'Institut Fourier %D 1994 %P 1435-1448 %V 44 %N 5 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.1440/ %R 10.5802/aif.1440 %G en %F AIF_1994__44_5_1435_0
Craizer, Marcos. Homogenization of codimension 1 actions of ${\mathbb {R}}^n$ near a compact orbit. Annales de l'Institut Fourier, Volume 44 (1994) no. 5, pp. 1435-1448. doi : 10.5802/aif.1440. http://archive.numdam.org/articles/10.5802/aif.1440/
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