Exponentially stable manifolds in the neighbourhood of elliptic equilibria

Antonio Giorgilli; Daniele Muraro

Bollettino dell'Unione Matematica Italiana (2006)

  • Volume: 9-B, Issue: 1, page 1-20
  • ISSN: 0392-4041

Abstract

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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.

How to cite

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Giorgilli, Antonio, and Muraro, Daniele. "Exponentially stable manifolds in the neighbourhood of elliptic equilibria." Bollettino dell'Unione Matematica Italiana 9-B.1 (2006): 1-20. <http://eudml.org/doc/289603>.

@article{Giorgilli2006,
abstract = {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.},
author = {Giorgilli, Antonio, Muraro, Daniele},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {1-20},
publisher = {Unione Matematica Italiana},
title = {Exponentially stable manifolds in the neighbourhood of elliptic equilibria},
url = {http://eudml.org/doc/289603},
volume = {9-B},
year = {2006},
}

TY - JOUR
AU - Giorgilli, Antonio
AU - Muraro, Daniele
TI - Exponentially stable manifolds in the neighbourhood of elliptic equilibria
JO - Bollettino dell'Unione Matematica Italiana
DA - 2006/2//
PB - Unione Matematica Italiana
VL - 9-B
IS - 1
SP - 1
EP - 20
AB - 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.
LA - eng
UR - http://eudml.org/doc/289603
ER -

References

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