Patrick Bernard (2002)
Annales de l’institut Fourier
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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.
John N. Mather (1993)
Annales de l'institut Fourier
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Patrick Bernard (2007)
Annales scientifiques de l'École Normale Supérieure
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R. Dieckerhoff, E. Zehnder (1987)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Diogo A. Gomes, Adam Oberman (2008)
ESAIM: Mathematical Modelling and Numerical Analysis
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The main objective of this paper is to prove new necessary conditions to the existence of KAM tori. To do so, we develop a set of explicit estimates for smooth solutions of Hamilton-Jacobi equations, using a combination of methods from viscosity solutions, KAM and Aubry-Mather theories. These estimates are valid in any space dimension, and can be checked numerically to detect gaps between KAM tori and Aubry-Mather sets. We apply these results to detect non-integrable regions in ...