Homogenization of codimension 1 actions of n near a compact orbit
Annales de l'Institut Fourier, Volume 44 (1994) no. 5, p. 1435-1448

Let Φ be a C n -action on an orientable (n+1)-dimensional manifold. Assume Φ has an isolated compact orbit T and let W be a small tubular neighborhood of it. By a C change of variables, we can write W= n / n ×I and T=𝕋 n ×[0], where I is some interval containing 0.

In this work, we show that by a C 0 change of variables, C outside T, we can make Φ |W invariant by transformations of the type (x,z)(x+a,z),a n , where x n / n and zI. As a corollary one cas describe completely the dynamics of Φ in W.

Soit Φ une n -action C sur une variété orientable de dimension n+1. Supposons que Φ possède une orbite compacte isolée T et soit W un petit voisinage tubulaire de T. À l’aide d’un changement de variables C , nous pouvons écrire W= n / n ×I et T= n / n ×[0], où I est un intervalle réel contenant 0.

Dans ce travail nous montrons que par un changement de variables C 0 , qui est C au-dehors de T, nous pouvons rendre Φ |W invariante par les transformations du type (x,z)(x+a,z),a n , où x n / n et zI. Comme corollaire nous pouvons décrire complètement la dynamique de Φ sur W.

     author = {Craizer, Marcos},
     title = {Homogenization of codimension 1 actions of ${\mathbb {R}}^n$ near a compact orbit},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {44},
     number = {5},
     year = {1994},
     pages = {1435-1448},
     doi = {10.5802/aif.1440},
     zbl = {0820.34021},
     mrnumber = {95m:58100},
     language = {en},
     url = {http://www.numdam.org/item/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://www.numdam.org/item/AIF_1994__44_5_1435_0/

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