Dynamical Systems
On the flat remainder in normal forms of families of analytic planar saddles
Comptes Rendus. Mathématique, Volume 346 (2008) no. 9-10, pp. 553-558.

We give an explicit expression for the (finitely) flat remainder after analytic normal form reduction of a family of planar saddles of diffeomorphisms or vector fields. We distinguish between a rational or irrational ratio of the moduli of the eigenvalues at the saddle for a certain value of the parameter.

Nous donnons une expression explicite du reste plat d'ordre fini, obtenue après une reduction analytique en forme normale, pur une famille de difféomorphismes ou de champs de vecteurs du plan ayant un point de selle à l'origine. Nous faisons la distinction entre un rapport rationnel ou irrationnel des modules des valuers propres pour une certaine valeur du paramètre.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2008.03.012
Bonckaert, Patrick 1; Verstringe, Freek 1

1 Hasselt University, Agoralaan, B-3590 Diepenbeek, Belgium
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Bonckaert, Patrick; Verstringe, Freek. On the flat remainder in normal forms of families of analytic planar saddles. Comptes Rendus. Mathématique, Volume 346 (2008) no. 9-10, pp. 553-558. doi : 10.1016/j.crma.2008.03.012. http://www.numdam.org/articles/10.1016/j.crma.2008.03.012/

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