no. 12
Differential Geometry/Dynamical Systems
Periodic orbits in the case of a zero eigenvalue
Presented by: Charles-Michel Marle
Birtea, Petre1; Puta, Mircea1; Tudoran, Răzvan Micu1
1Seminarul 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

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:
Accepted:
Published online:
DOI: 10.1016/j.crma.2007.05.003

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

1 Seminarul de Geometrie şi Topologie, West University of Timişoara, B-dul V. Pârvan no 4, 300223 Timişoara, Romania 
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Birtea, Petre; Puta, Mircea; Tudoran, Răzvan Micu. 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

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

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

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

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

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