Periodic orbits in the case of a zero eigenvalue

Petre Birtea; Mircea Puta; Răzvan Micu Tudoran

doi:10.1016/j.crma.2007.05.003

Differential Geometry/Dynamical Systems

Periodic orbits in the case of a zero eigenvalue

Presented by: Charles-Michel Marle

Petre Birtea ¹; Mircea Puta ¹; Răzvan Micu Tudoran ¹

¹ Seminarul de Geometrie şi Topologie, West University of Timişoara, B-dul V. Pârvan no 4, 300223 Timişoara, Romania

Comptes Rendus. Mathématique, Volume 344 (2007) no. 12, pp. 779-784.

Abstract
Résumé

We will show that if a dynamical system has enough constants of motion then a Moser–Weinstein type theorem can be applied for proving the existence of periodic orbits in the case when the linearized system is degenerate.

On va montrer que si un système dynamique a assez d'intégrales premières, alors on peut utiliser un théorème de type Moser–Weinstein pour prouver l'existence d'orbites périodiques, même si le système linéarisé associé est dégénéré.

Received: 2006-07-31
Accepted: 2007-05-10
Published online: 2007-06-15

DOI: 10.1016/j.crma.2007.05.003

Author's affiliations:

Petre Birtea ¹; Mircea Puta ¹; Răzvan Micu Tudoran ¹

¹ Seminarul de Geometrie şi Topologie, West University of Timişoara, B-dul V. Pârvan no 4, 300223 Timişoara, Romania

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     author = {Petre Birtea and Mircea Puta and R\u{a}zvan Micu Tudoran},
     title = {Periodic orbits in the case of a zero eigenvalue},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {779--784},
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     doi = {10.1016/j.crma.2007.05.003},
     language = {en},
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Petre Birtea; Mircea Puta; Răzvan Micu Tudoran. Periodic orbits in the case of a zero eigenvalue. Comptes Rendus. Mathématique, Volume 344 (2007) no. 12, pp. 779-784. doi : 10.1016/j.crma.2007.05.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.05.003/

References
Cited by

[1] B. Dubrovin; I. Krichever; S. Novikov Integrable Systems, Encyclopedia of Math. Sci., vol. 4, Springer-Verlag, Berlin, 1990, pp. 173-280

[2] M.A. Lyapunov Problème général de la stabilité du mouvement, Ann. Fac. Sci. Toulouse, Volume 2 (1907), pp. 203-474

[3] J. Moser Periodic orbits and a theorem by Alan Weinstein, Comm. Pure Appl. Math., Volume 29 (1976), pp. 727-747

[4] A. Weinstein Normal modes for non-linear Hamiltonian systems, Invent. Math., Volume 20 (1973), pp. 47-57

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