Uniqueness of invariant Lagrangian graphs in a homology or a cohomology class

Annali della Scuola Normale - Classe di Scienze

Volumn 8, Issue 4, 2009, Pages 659-680

  Fathi, Albert ^a   Giuliani, Alessandro ^b   Sorrentino, Alfonso ^c,d  

^a UNITÉ DE MATHÉMATIQUES PURES ET APPLIQUÉES   (France)

^b ROMA TRE UNIVERSITY   (Italy)

^c PRINCETON UNIVERSITY   (United States)

^d UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77952701371     PISSN: 0391173X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (28)

1. V. I. ARNOL'D, Proof of a theorem of A. N. Kolmogorov on the preservation of conditionally periodic motions under a small perturbation of the Hamiltonian, Uspekhi Mat. Nauk 5(113) 18(1963), 13-40.
2. A. BANYAGA, "The Structure of Classical Diffeomorphism Groups", Mathematics and its Applications, Vol.400, Kluwer Academic Publishers Group, Dordrecht, 1997.
3. 1,1 critical subsolutions of the Hamilton-Jacobi equation on compact manifolds, Ann. Sci. École Norm. Sup. (3) 40 (2007), 445-452.
4. G. D. BIRKHOFF, Surface transformations and their dynamical applications. Acta Math. (1) 43 (1920);
5. Sur quelques courbes fermées remarquables, Bull. Soc. Math. France (1) 60 (1932);
6. reprinted in Collected Mathematical Papers, Vol.II, 111-418, respectively (New York: AMS 1950).
7. H. BROER and F. TAKENS, Unicity of KAM tori; Ergodic Theory Dynam. Systems (3) 27 (2007), 713-724.
8. M. J. DIAS CARNEIRO, On minimizing measures of the action of autonomous Lagrangians, Nonlinearity (6) 8 (1995), 1077-1085.
9. O. COSTIN, G. GALLAVOTTI, G. GENTILE and A. GIULIANI, Borel summability and Lindstedt series, Comm. Math. Phys. (1) 269 (2007), 175-193.
10. G. CONTRERAS and R. ITURRIAGA, Global minimizers of autonomous Lagrangians. In: "22° Colóquio Brasileiro de Matemática" [22nd Brazilian Mathematics Colloquium]. Instituto de Matemática Pura e Aplicada (IMPA), Rio de Janeiro, 1999,148 pp.
11. A. FATHI, Structure of the group of homeomorphisms preserving a good measure on a compact manifold, Ann. Sci. École Norm. Sup. (4) 13 (1980), 45-93.
12. A. FATHI, "The Weak KAM Theorem in Lagrangian Dynamics", Cambridge University Press, to appear.
13. A. FATHI and M. R. HERMAN, Existence de difféomorphismes minimaux. Astérisque 49 (1977), 37-59.
14. 1 critical subsolutions of the Hamilton-Jacobi equation. Invent. Math. (2) 155 (2004), 363-388.
15. G. GALLAVOTTI and G. GENTILE , Hyperbolic low-dimensional invariant tori and summations of divergent series, Comm. Math. Phys. (3) 227 (2002), 421-460.
16. G. GENTILE and G. GALLAVOTTI, Degenerate elliptic resonances, Comm. Math. Phys. (2) 257 (2005), 319-362.
17. M. R. HERMAN, Inégalités "a priori" pour des tores lagrangiens invariants par des difféomorphismes symplectiques, Inst. Hautes Études Sci. Publ. Math. 70 (1989), 47-101.
18. M. R. HERMAN, On the dynamics of Lagrangian tori invariant by symplectic diffeomorphisms, In: "Progress in variational methods in Hamiltonian systems and elliptic equations" (L' Aquila, 1990), Pitman Res. Notes Math. Ser., 243, Longman Sci. Tech., Harlow, 1992, 92-112.
19. A. N. KOLMOGOROV, On conservation of conditionally periodic motions for a small change in Hamilton's function, Dokl. Akad. Nauk SSSR (N.S.) 98 (1954), 527-530.
20. P.-L. LIONS, G. PAPANICOLAOU and S. R. SRINIVASA VARADHAN, Homogenization of Hamilton-Jacobi equation. Unpublished preprint, 1987.
21. R. MAÑÉ, Lagrangian flows: the dynamics of globally minimizing orbits, Bol. Soc. Brasil. Mat. (N.S.) (2) 28 (1997), 141-153.
22. J. N. MATHER, Action minimizing invariant measures for positive definite Lagrangian systems. Math. Z. (2) 207 (1991), 169-207.
23. J. N. MATHER, Variational construction of connecting orbits, Ann. Inst. Fourier (Grenoble) (5)43(1993), 1349-1386.
24. J. MOSER, On invariant curves of area-preserving mappings of an annulus, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II, (1962), 1-20.
25. D. SALAMON and E. ZEHNDER, KAM theory in configuration space. Comment. Math. Helv. (1)64 (1989), 84-132.
26. D. A. SALAMON, The Kolmogorov-Arnold-Moser theorem, Math. Phys. Electron. J. 10: Paper 3, 37 pp. (electronic), 2004.
27. S. SCHWARTZMAN, Asymptotic cycles, Ann. of Math. (2) 66 (1957), 270-284.
28. A. SORRENTINO, On the integrability of Tonelli Hamiltonians, preprint (2009), arXiV:0903.4300.