Homogenization of codimension 1 actions of ${ℝ}^n$ near a compact orbit

@article{Craizer1994,
abstract = {Let $\Phi $ be a $C^\infty \,\{\Bbb R\}^n$-action on an orientable $(n+1)$-dimensional manifold. Assume $\Phi $ has an isolated compact orbit $T$ and let $W$ be a small tubular neighborhood of it. By a $C^\infty $ change of variables, we can write $W=\{\Bbb R\}^n/\{\Bbb Z\}^n\times I$ and $T=\{\Bbb T\}^n\times [0]$, where $I$ is some interval containing 0.In this work, we show that by a $C^0$ change of variables, $C^\infty $ outside $T$, we can make $\Phi _\{\vert W\}$ invariant by transformations of the type $(x,z)\rightarrow (x+a,z),\, a\in \{\Bbb R\}^n$, where $x\in \{\Bbb R\}^n/\{\Bbb Z\}^n$ and $z\in I$. As a corollary one cas describe completely the dynamics of $\Phi $ in $W$.},
author = {Craizer, Marcos},
journal = {Annales de l'institut Fourier},
keywords = {homogenization; codimension 1 actions of ; compact orbit; return times},
language = {eng},
number = {5},
pages = {1435-1448},
publisher = {Association des Annales de l'Institut Fourier},
title = {Homogenization of codimension 1 actions of $\{\mathbb \{R\}\}^n$ near a compact orbit},
url = {http://eudml.org/doc/75104},
volume = {44},
year = {1994},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 44
IS - 5
SP - 1435
EP - 1448
AB - Let $\Phi $ be a $C^\infty \,{\Bbb R}^n$-action on an orientable $(n+1)$-dimensional manifold. Assume $\Phi $ has an isolated compact orbit $T$ and let $W$ be a small tubular neighborhood of it. By a $C^\infty $ change of variables, we can write $W={\Bbb R}^n/{\Bbb Z}^n\times I$ and $T={\Bbb T}^n\times [0]$, where $I$ is some interval containing 0.In this work, we show that by a $C^0$ change of variables, $C^\infty $ outside $T$, we can make $\Phi _{\vert W}$ invariant by transformations of the type $(x,z)\rightarrow (x+a,z),\, a\in {\Bbb R}^n$, where $x\in {\Bbb R}^n/{\Bbb Z}^n$ and $z\in I$. As a corollary one cas describe completely the dynamics of $\Phi $ in $W$.
LA - eng
KW - homogenization; codimension 1 actions of ; compact orbit; return times
UR - http://eudml.org/doc/75104
ER -