[Temps et relation entrée–sortie proche d'un point tournant planaire.]
Suivant l'approche géométrique dans l'étude de problèmes de perturbations singulières dans le plan aux points tournants, et travaillant dans un cadre très général dans lequel apparaissent des solutions canards, nous étudions le temps de passage des orbites proche des points tournants, tout comme la relation entrée–sortie à tel point. Les variétés de solutions canards rencontrées ne sont en général que à un point tournant, ne permettant pas une approche asymptotique classique. L'approche est basée sur l'éclatement et l'utilisation de variétés centrales et de formes normales .
Following the geometric approach for studying singular perturbation problems in the plane at turning points, and considering a very general setting where canard solutions are shown to exist, we study the transition time of orbits passing near the turning point, as well as the entry–exit relation at such turning points. The manifolds of canard solutions are in general only at the turning point, making the classical asymptotic approach impossible. The method involves a (family) blow up of the turning point and the use of -normal forms and center manifolds.
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@article{CRMATH_2004__339_5_359_0,
author = {De Maesschalck, Peter and Dumortier, Freddy},
title = {Time and entry{\textendash}exit relation near a planar turning point},
journal = {Comptes Rendus. Math\'ematique},
pages = {359--364},
publisher = {Elsevier},
volume = {339},
number = {5},
year = {2004},
doi = {10.1016/j.crma.2004.06.020},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2004.06.020/}
}
TY - JOUR AU - De Maesschalck, Peter AU - Dumortier, Freddy TI - Time and entry–exit relation near a planar turning point JO - Comptes Rendus. Mathématique PY - 2004 SP - 359 EP - 364 VL - 339 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2004.06.020/ DO - 10.1016/j.crma.2004.06.020 LA - en ID - CRMATH_2004__339_5_359_0 ER -
%0 Journal Article %A De Maesschalck, Peter %A Dumortier, Freddy %T Time and entry–exit relation near a planar turning point %J Comptes Rendus. Mathématique %D 2004 %P 359-364 %V 339 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2004.06.020/ %R 10.1016/j.crma.2004.06.020 %G en %F CRMATH_2004__339_5_359_0
De Maesschalck, Peter; Dumortier, Freddy. Time and entry–exit relation near a planar turning point. Comptes Rendus. Mathématique, Tome 339 (2004) no. 5, pp. 359-364. doi : 10.1016/j.crma.2004.06.020. http://www.numdam.org/articles/10.1016/j.crma.2004.06.020/
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