Dynamical Systems
Time and entry–exit relation near a planar turning point
Comptes Rendus. Mathématique, Volume 339 (2004) no. 5, pp. 359-364.

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 C0 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 Ck-normal forms and center manifolds.

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 C0 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 Ck.

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Accepted:
Published online:
DOI: 10.1016/j.crma.2004.06.020
De Maesschalck, Peter 1; Dumortier, Freddy 1

1 Limburgs Universitair Centrum, 3590 Diepenbeek, Belgium
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De Maesschalck, Peter; Dumortier, Freddy. Time and entry–exit relation near a planar turning point. Comptes Rendus. Mathématique, Volume 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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[3] F. Dumortier, P. De Maesschalck, Time analysis and entry–exit relation near planar turning points, 2004, preprint

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