Tame semiflows for piecewise linear vector fields

Panazzolo, Daniel. "Tame semiflows for piecewise linear vector fields." Annales de l’institut Fourier 52.6 (2002): 1593-1628. <http://eudml.org/doc/116021>.

@article{Panazzolo2002,
abstract = {Let $\{\mathcal \{E\}\}$ be a disjoint decomposition of $\{\mathbb \{R\}\}^n$ and let $X$ be a vector field on $\{\mathbb \{R\}\}^n$, defined to be linear on each cell of the decomposition $\{\mathcal \{E\}\}$. Under some natural assumptions, we show how to associate a semiflow to $X$ and prove that such semiflow belongs to the o-minimal structure $\{\mathbb \{R\}\}_\{\{\rm an\},\exp \}$. In particular, when $X$ is a continuous vector field and $\Gamma $ is an invariant subset of $X$, our result implies that if $\Gamma $ is non-spiralling then the Poincaré first return map associated $\Gamma $ is also in $\{\mathbb \{R\}\}_\{\{\rm an\} ,\exp \}$.},
affiliation = {Universidade de São Paulo, Dep. Matemática Aplicada, Rua do Matao, 1010, São Paulo 05508-090 (Brésil)},
author = {Panazzolo, Daniel},
journal = {Annales de l’institut Fourier},
keywords = {piecewise linear vector field; o-minimal; semiflow; o-minimal structure},
language = {eng},
number = {6},
pages = {1593-1628},
publisher = {Association des Annales de l'Institut Fourier},
title = {Tame semiflows for piecewise linear vector fields},
url = {http://eudml.org/doc/116021},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Panazzolo, Daniel
TI - Tame semiflows for piecewise linear vector fields
JO - Annales de l’institut Fourier
PY - 2002
PB - Association des Annales de l'Institut Fourier
VL - 52
IS - 6
SP - 1593
EP - 1628
AB - Let ${\mathcal {E}}$ be a disjoint decomposition of ${\mathbb {R}}^n$ and let $X$ be a vector field on ${\mathbb {R}}^n$, defined to be linear on each cell of the decomposition ${\mathcal {E}}$. Under some natural assumptions, we show how to associate a semiflow to $X$ and prove that such semiflow belongs to the o-minimal structure ${\mathbb {R}}_{{\rm an},\exp }$. In particular, when $X$ is a continuous vector field and $\Gamma $ is an invariant subset of $X$, our result implies that if $\Gamma $ is non-spiralling then the Poincaré first return map associated $\Gamma $ is also in ${\mathbb {R}}_{{\rm an} ,\exp }$.
LA - eng
KW - piecewise linear vector field; o-minimal; semiflow; o-minimal structure
UR - http://eudml.org/doc/116021
ER -