Formal normal form of $ {A}_{k}$ slow–fast systems

Hildeberto Jardón-Kojakhmetov

doi:10.1016/j.crma.2015.06.009

Ordinary differential equations/Dynamical systems

Formal normal form of

A_{k}

slow–fast systems
[Forme normale formelle des systèmes lents–rapides de type

A_{k}

]

Présenté par : the Editorial Board

Hildeberto Jardón-Kojakhmetov ¹

¹ Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, P.O. Box 407, 9700 AK, Groningen, The Netherlands

Comptes Rendus. Mathématique, Volume 353 (2015) no. 9, pp. 795-800.

Résumé
Abstract

Un système lent–rapide de type $A_{k}$ est une équation différentielle ordinaire singulièrement perturbée avec une structure particulière. La varieté lente correspondante est définie par les points critiques d'un déploiment universel d'une singularité de type $A_{k}$ . Dans cette note, nous proposons une forme normale formelle des systèmes lents–rapides de type $A_{k}$ .

An $A_{k}$ slow–fast system is a particular type of singularly perturbed ODE. The corresponding slow manifold is defined by the critical points of a universal unfolding of an $A_{k}$ singularity. In this note we propose a formal normal form of $A_{k}$ slow–fast systems.

Reçu le : 2015-03-18
Accepté le : 2015-06-25
Publié le : 2015-07-16

DOI : 10.1016/j.crma.2015.06.009

Affiliations des auteurs :

Hildeberto Jardón-Kojakhmetov ¹

¹ Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, P.O. Box 407, 9700 AK, Groningen, The Netherlands

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     author = {Hildeberto Jard\'on-Kojakhmetov},
     title = {Formal normal form of $ {A}_{k}$ slow{\textendash}fast systems},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {795--800},
     publisher = {Elsevier},
     volume = {353},
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     doi = {10.1016/j.crma.2015.06.009},
     language = {en},
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Hildeberto Jardón-Kojakhmetov. Formal normal form of $ {A}_{k}$ slow–fast systems. Comptes Rendus. Mathématique, Volume 353 (2015) no. 9, pp. 795-800. doi : 10.1016/j.crma.2015.06.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.06.009/

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