Soit une décomposition disjointe de et soit un champ de vecteurs sur , défini comme étant linéaire sur chaque cellule de la décomposition . Sous certaines hypothèses naturelles, nous montrons comment associer un semi-flot à et nous montrons qu’un tel semi-flot appartient à la structure o-minimale . En particulier, si est un champ de vecteurs continu et est un sous-ensemble invariant par , notre résultat implique que l’application de premier retour de Poincaré associée à est également dans quand est non-spiralante.
Let be a disjoint decomposition of and let be a vector field on , defined to be linear on each cell of the decomposition . Under some natural assumptions, we show how to associate a semiflow to and prove that such semiflow belongs to the o-minimal structure . In particular, when is a continuous vector field and is an invariant subset of , our result implies that if is non-spiralling then the Poincaré first return map associated is also in .
@article{AIF_2002__52_6_1593_0, author = {Panazzolo, Daniel}, title = {Tame semiflows for piecewise linear vector fields}, journal = {Annales de l'Institut Fourier}, volume = {52}, year = {2002}, pages = {1593-1628}, doi = {10.5802/aif.1928}, mrnumber = {1952525}, zbl = {1009.37008}, language = {en}, url = {http://dml.mathdoc.fr/item/AIF_2002__52_6_1593_0} }
Panazzolo, Daniel. Tame semiflows for piecewise linear vector fields. Annales de l'Institut Fourier, Tome 52 (2002) pp. 1593-1628. doi : 10.5802/aif.1928. http://gdmltest.u-ga.fr/item/AIF_2002__52_6_1593_0/
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