no. 5
Connecting orbits of time dependent Lagrangian systems
[Connexions dans les systèmes lagrangiens dépendant du temps]
Bernard, Patrick1
1 Université Joseph Fourier, Institut Fourier, BP 74, 38402 Saint-Martin d'Hères Cedex (France)
Annales de l'Institut Fourier, Tome 52 (2002) no. 5, pp. 1533-1568.

On donne une généralisation à la dimension supérieure des résultats obtenus par Birkhoff et Mather sur l'existence d'orbites errant dans les zones d'instabilité des applications de l'anneau déviant la verticale. Notre généralisation s'inspire fortement de celle proposée par Mather. Elle présente cependant l'avantage de contenir effectivement l'essentiel des résultats de Birkhoff et Mather sur les difféomorphismes de l'anneau.

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.

DOI : 10.5802/aif.1924
Classification : 37J45, 37J50, 53D99, 35F99
Keywords: connecting orbits, lagrangian systems, minimizing orbits
Mot clés : orbites hétéroclines, systèmes lagrangiens, orbites minimisantes

Bernard, Patrick 1

1 Université Joseph Fourier, Institut Fourier, BP 74, 38402 Saint-Martin d'Hères Cedex (France) 
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Bernard, Patrick. Connecting orbits of time dependent Lagrangian systems. Annales de l'Institut Fourier, Tome 52 (2002) no. 5, pp. 1533-1568. doi : 10.5802/aif.1924. https://aif.centre-mersenne.org/articles/10.5802/aif.1924/

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