[Sur le reste plat de la forme normale d'une famille de points de selle analytiques dans le plan]
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.
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.
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@article{CRMATH_2008__346_9-10_553_0,
author = {Bonckaert, Patrick and Verstringe, Freek},
title = {On the flat remainder in normal forms of families of analytic planar saddles},
journal = {Comptes Rendus. Math\'ematique},
pages = {553--558},
publisher = {Elsevier},
volume = {346},
number = {9-10},
year = {2008},
doi = {10.1016/j.crma.2008.03.012},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2008.03.012/}
}
TY - JOUR AU - Bonckaert, Patrick AU - Verstringe, Freek TI - On the flat remainder in normal forms of families of analytic planar saddles JO - Comptes Rendus. Mathématique PY - 2008 SP - 553 EP - 558 VL - 346 IS - 9-10 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2008.03.012/ DO - 10.1016/j.crma.2008.03.012 LA - en ID - CRMATH_2008__346_9-10_553_0 ER -
%0 Journal Article %A Bonckaert, Patrick %A Verstringe, Freek %T On the flat remainder in normal forms of families of analytic planar saddles %J Comptes Rendus. Mathématique %D 2008 %P 553-558 %V 346 %N 9-10 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2008.03.012/ %R 10.1016/j.crma.2008.03.012 %G en %F CRMATH_2008__346_9-10_553_0
Bonckaert, Patrick; Verstringe, Freek. On the flat remainder in normal forms of families of analytic planar saddles. Comptes Rendus. Mathématique, Tome 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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