Symplectic aspects of mather theory

Duke Mathematical Journal

Volumn 136, Issue 3, 2007, Pages 401-420

  Bernard, Patrick ^a  

^a UNIVERSITÉ PARIS DAUPHINE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33847632207     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-07-13631-7     Document Type: Article

References (18)

1. P. BERNARD, Connecting orbits of time dependent Lagrangian systems, Ann. Inst. Fourier (Grenoble) 52 (2002), 1533-1568. MR 1935556
2. _, The action spectrum near positive definite invariant tori, Bull. Soc. Math. France 131 (2003), 603-616. MR 2044497
3. _, The dynamics of pseudographs in convex Hamiltonian systems, preprint, arXiv:math.DS/0412300
4. C.-Q. CHENG and J. VAN, Existence of diffusion orbits in a priori unstable Hamiltonian systems, J. Differential Geom. 67 (2004), 457-517. MR 2153027
5. _, Arnold diffusion in Hamiltonian systems, 1: A priori unstable case, preprint, 2005.
6. G. CONTRERAS, J. DELGADO, and R. ITURRIAGA, Lagrangian flows: The dynamics of globally minimizing orbits, II, Bol. Soc. Brasil. Mat. (N.S.) 28 (1997), 155-196. MR 1479500
7. A. FATHI, Solutions KAM faibles conjuguées et barrières de Peierls, C. R. Acad. Sci. Paris Sér. I Math. 325 (1997), 649-652. MR 1473840
8. _, Théorème KAM faible et théorie de Mather sur les systèmes lagrangiens, C. R. Acad. Sci. Paris Sér. I Math. 324 (1997), 1043-1046. MR 1451248
9. _, Weak KAM Theory in Lagrangian Dynamics, in preparation.
10. R. MAÑÉ, Lagrangian flows: The dynamics of globally minimizing orbits. Bol. Soc. Brasil. Mat. (N.S.) 28 (1997), 141-153. MR 1479499
11. J. N. MATHER, Action minimizing invariant measures for positive definite Lagrangian systems, Math. Z. 207 (1991), 169-207. MR 1109661
12. _, Variational construction of orbits of twist diffeomorphisms, J. Amer. Math. Soc. 4 (1991), 207-263. MR 1080112
13. _, Variational construction of connecting orbits, Ann. Inst. Fourier (Grenoble) 43 (1993), 1349-1386. MR 1275203
14. G. P. PATERNAIN, L. POLTEROVICH, and K. F. SIBURG, Boundary rigidity for Lagrangian submanifolds, non-removable intersections, and Aubry-Mather theory, Mosc. Math. J. 3, no. 2 (2003), 593-619. MR 2025275
15. K. F. SIBURG, Symplectic invariants of elliptic fixed points, Comment. Math. Helv. 75 (2000), 681-700. MR 1789182
16. _, The Principle of Least Action in Geometry and Dynamics, Lecture Notes in Math. 1844, Springer, Berlin, 2004. MR 2076302
17. Z. XIA, "Arnold diffusion: A variational construction" in Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998), Doc. Math. 1998, Extra Vol. II, 867-877. MR 1648133
18. _, Arnold diffusion and instabilities in Hamiltonian dynamics, preprint, 2002.