Connecting orbits of time dependent Lagrangian systems

Patrick Bernard[1]

  • [1] Université Joseph Fourier, Institut Fourier, BP 74, 38402 Saint-Martin d'Hères Cedex (France)

Annales de l’institut Fourier (2002)

  • Volume: 52, Issue: 5, page 1533-1568
  • ISSN: 0373-0956

Abstract

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We generalize to higher dimension results of Birkhoff and Mather on the existence of orbits wandering in regions of instability of twist maps. This generalization is strongly inspired by the one proposed by Mather. However, its advantage is that it contains most of the results of Birkhoff and Mather on twist maps.

How to cite

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Bernard, Patrick. "Connecting orbits of time dependent Lagrangian systems." Annales de l’institut Fourier 52.5 (2002): 1533-1568. <http://eudml.org/doc/116017>.

@article{Bernard2002,
abstract = {We generalize to higher dimension results of Birkhoff and Mather on the existence of orbits wandering in regions of instability of twist maps. This generalization is strongly inspired by the one proposed by Mather. However, its advantage is that it contains most of the results of Birkhoff and Mather on twist maps.},
affiliation = {Université Joseph Fourier, Institut Fourier, BP 74, 38402 Saint-Martin d'Hères Cedex (France)},
author = {Bernard, Patrick},
journal = {Annales de l’institut Fourier},
keywords = {connecting orbits; lagrangian systems; minimizing orbits; Lagrangian systems},
language = {eng},
number = {5},
pages = {1533-1568},
publisher = {Association des Annales de l'Institut Fourier},
title = {Connecting orbits of time dependent Lagrangian systems},
url = {http://eudml.org/doc/116017},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Bernard, Patrick
TI - Connecting orbits of time dependent Lagrangian systems
JO - Annales de l’institut Fourier
PY - 2002
PB - Association des Annales de l'Institut Fourier
VL - 52
IS - 5
SP - 1533
EP - 1568
AB - We generalize to higher dimension results of Birkhoff and Mather on the existence of orbits wandering in regions of instability of twist maps. This generalization is strongly inspired by the one proposed by Mather. However, its advantage is that it contains most of the results of Birkhoff and Mather on twist maps.
LA - eng
KW - connecting orbits; lagrangian systems; minimizing orbits; Lagrangian systems
UR - http://eudml.org/doc/116017
ER -

References

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  10. J. Mather, Action minimizing invariant measures for positive definite Lagrangian systems, Math. Z 207 (1991), 169-207 Zbl0696.58027MR1109661
  11. J. Mather, Variational construction of connecting orbits, Ann. Inst. Fourier (1993) Zbl0803.58019MR1275203
  12. J. Mather, G. Forni, Action minimizing orbits in Hamiltonian systems, Transition to chaos in classical and quantum mechanics 1589 (1994), Springer Zbl0822.70011
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