Geodesic
Exponentially stable manifolds in the neighbourhood of elliptic equilibria
Bollettino della Unione matematica italiana, Série 8, 9B (2006) no. 1, pp. 1-20

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

We consider a Hamiltonian system in a neighbourhood of an elliptic equilibrium which is a minimum for the Hamiltonian. With appropriate non-resonance conditions we prove that in the neighbourhood of the equilibrium there exist low dimensional manifolds that are exponentially stable in Nekhoroshev’s sense. This generalizes the theorem of Lyapounov on the existence of periodic orbits. The result may be meaningful for, e.g., the dynamics of non-linear chains of the Fermi-Pasta-Ulam (FPU) type. 
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     author = {Giorgilli, Antonio and Muraro, Daniele},
     title = {Exponentially stable manifolds in the neighbourhood of elliptic equilibria},
     journal = {Bollettino della Unione matematica italiana},
     pages = {1--20},
     publisher = {mathdoc},
     volume = {Ser. 8, 9B},
     number = {1},
     year = {2006},
     zbl = {1178.70084},
     mrnumber = {MR2204898},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2006_8_9B_1_a0/}
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Giorgilli, Antonio; Muraro, Daniele. Exponentially stable manifolds in the neighbourhood of elliptic equilibria. Bollettino della Unione matematica italiana, Série 8, 9B (2006) no. 1, pp. 1-20. http://geodesic.mathdoc.fr/item/BUMI_2006_8_9B_1_a0/