no. 6
Tame semiflows for piecewise linear vector fields
[Semi-flots pour des champs de vecteurs linéaires morcelés]
Panazzolo, Daniel1
1 Universidade de São Paulo, Dep. Matemática Aplicada, Rua do Matao, 1010, São Paulo 05508-090 (Brésil)
Annales de l'Institut Fourier, Tome 52 (2002) no. 6, pp. 1593-1628.

Soit ℰ une décomposition disjointe de ℝ n et soit X un champ de vecteurs sur ℝ n , défini comme étant linéaire sur chaque cellule de la décomposition ℰ. Sous certaines hypothèses naturelles, nous montrons comment associer un semi-flot à X et nous montrons qu’un tel semi-flot appartient à la structure o-minimale ℝ an ,exp . En particulier, si X est un champ de vecteurs continu et Γ est un sous-ensemble invariant par X, notre résultat implique que l’application de premier retour de Poincaré associée à Γ est également dans ℝ an ,exp quand Γ est non-spiralante.

Let ℰ be a disjoint decomposition of ℝ n and let X be a vector field on ℝ n , defined to be linear on each cell of the decomposition ℰ. Under some natural assumptions, we show how to associate a semiflow to X and prove that such semiflow belongs to the o-minimal structure ℝ an ,exp . In particular, when X is a continuous vector field and Γ is an invariant subset of X, our result implies that if Γ is non-spiralling then the Poincaré first return map associated Γ is also in ℝ an ,exp .

DOI : 10.5802/aif.1928
Classification : 03C64, 14P10, 34C25, 37G15
Keywords: piecewise linear vector field, o-minimal, semiflow
Mot clés : champ de vecteurs linéaire par parties, o-minimale, semi-flot

Panazzolo, Daniel 1

1 Universidade de São Paulo, Dep. Matemática Aplicada, Rua do Matao, 1010, São Paulo 05508-090 (Brésil) 
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Panazzolo, Daniel. Tame semiflows for piecewise linear vector fields. Annales de l'Institut Fourier, Tome 52 (2002) no. 6, pp. 1593-1628. doi : 10.5802/aif.1928. https://aif.centre-mersenne.org/articles/10.5802/aif.1928/

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