On sub-harmonic bifurcations

Marc Chaperon; Santiago López de Medrano; José Lino Samaniego

doi:10.1016/j.crma.2005.04.017

Dynamical Systems/Ordinary Differential Equations

On sub-harmonic bifurcations

Presented by: Étienne Ghys

Marc Chaperon ¹; Santiago López de Medrano ²; José Lino Samaniego ³

¹ Institut de mathématiques de Jussieu & université Paris 7, UFR de mathématiques, case 7012, 2, place Jussieu, 75251 Paris cedex 05, France
² Facultad de Ciencias & Instituto de Matemáticas, UNAM, Ciudad Universitaria, México, D.F., 04510, Mexico
³ Departamento de Matemáticas, Facultad de Ciencias, Ciudad Universitaria, México, D.F., 04510, Mexico

Comptes Rendus. Mathématique, Volume 340 (2005) no. 11, pp. 827-832

Abstract (Original language)
Résumé

Under fairly general hypotheses, we investigate by elementary methods the structure of the p-periodic orbits of a family $h_{u}$ of transformations near $(u_{0}, x_{0})$ when $h_{u_{0}} (x_{0}) = x_{0}$ and $d h_{u_{0}} (x_{0})$ has a simple eigenvalue which is a primitive p-th root of unity.

Sous des hypothèses très générales, nous étudions par des méthodes élémentaires la structure de l'ensemble des orbites de période p d'une famille $h_{u}$ de transformations au voisinage de $(u_{0}, x_{0})$ lorsque $h_{u_{0}} (x_{0}) = x_{0}$ et que $d h_{u_{0}} (x_{0})$ a une valeur propre simple racine primitive p-ième de l'unité.

Received: 2005-03-12
Accepted: 2005-04-03
Published online: 2005-05-13

DOI: 10.1016/j.crma.2005.04.017

Author's affiliations:

Marc Chaperon ¹; Santiago López de Medrano ²; José Lino Samaniego ³

¹ Institut de mathématiques de Jussieu & université Paris 7, UFR de mathématiques, case 7012, 2, place Jussieu, 75251 Paris cedex 05, France
² Facultad de Ciencias & Instituto de Matemáticas, UNAM, Ciudad Universitaria, México, D.F., 04510, Mexico
³ Departamento de Matemáticas, Facultad de Ciencias, Ciudad Universitaria, México, D.F., 04510, Mexico

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     author = {Marc Chaperon and Santiago L\'opez de Medrano and Jos\'e Lino Samaniego},
     title = {On sub-harmonic bifurcations},
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     number = {11},
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     language = {en},
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Marc Chaperon; Santiago López de Medrano; José Lino Samaniego. On sub-harmonic bifurcations. Comptes Rendus. Mathématique, Volume 340 (2005) no. 11, pp. 827-832. doi: 10.1016/j.crma.2005.04.017

References
Cited by

[1] M. Chaperon, S. López de Medrano, On the Hopf bifurcation for flows, C. R. Acad. Sci. Paris, Ser. I 340 (2005), in press

[2] J.L. Samaniego, Tesis Doctoral, UNAM, to be defended

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