Connecting orbits of time dependent Lagrangian systems
Annales de l'Institut Fourier, Volume 52 (2002) no. 5, p. 1533-1568
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.
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.
DOI : https://doi.org/10.5802/aif.1924
Classification:  37J45,  37J50,  53D99,  35F99
Keywords: connecting orbits, lagrangian systems, minimizing orbits
@article{AIF_2002__52_5_1533_0,
     author = {Bernard, Patrick},
     title = {Connecting orbits of time dependent Lagrangian systems},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {52},
     number = {5},
     year = {2002},
     pages = {1533-1568},
     doi = {10.5802/aif.1924},
     mrnumber = {1935556},
     zbl = {1008.37035},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2002__52_5_1533_0}
}
Bernard, Patrick. Connecting orbits of time dependent Lagrangian systems. Annales de l'Institut Fourier, Volume 52 (2002) no. 5, pp. 1533-1568. doi : 10.5802/aif.1924. https://aif.centre-mersenne.org/item/AIF_2002__52_5_1533_0/

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