Tame semiflows for piecewise linear vector fields
Annales de l'Institut Fourier, Volume 52 (2002) no. 6, pp. 1593-1628.

Let be a disjoint decomposition of n and let X be a vector field on n , defined to be linear on each cell of the decomposition . Under some natural assumptions, we show how to associate a semiflow to X and prove that such semiflow belongs to the o-minimal structure 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 an ,exp .

Soit une décomposition disjointe de n et soit X un champ de vecteurs sur n , défini comme étant linéaire sur chaque cellule de la décomposition . 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 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 an ,exp quand Γ est non-spiralante.

DOI: 10.5802/aif.1928
Classification: 03C64, 14P10, 34C25, 37G15
Keywords: piecewise linear vector field, o-minimal, semiflow
Panazzolo, Daniel 1

1 Universidade de São Paulo, Dep. Matemática Aplicada, Rua do Matao, 1010, São Paulo 05508-090 (Brésil)
     author = {Panazzolo, Daniel},
     title = {Tame semiflows for piecewise linear vector fields},
     journal = {Annales de l'Institut Fourier},
     pages = {1593--1628},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {52},
     number = {6},
     year = {2002},
     doi = {10.5802/aif.1928},
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Panazzolo, Daniel. Tame semiflows for piecewise linear vector fields. Annales de l'Institut Fourier, Volume 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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