Existence of diffusion orbits in a priori unstable hamiltonian systems

Journal of Differential Geometry

Volumn 67, Issue 3, 2004, Pages 457-517

  Cheng, Chong Qing ^a   Yan, Jun ^b  

^a NANJING UNIVERSITY   (China)

^b FUDAN UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33744991766     PISSN: 0022040X     EISSN: 1945743X     Source Type: Journal    
DOI: 10.4310/jdg/1102091356     Document Type: Article

References (20)

1. V.I. Arnol’d, Instability of dynamical systems with several degrees of freedom (Russian, English), Sov. Math., Dokl. 5 (1964) 581-585
2. V.I. Arnol’d, Instability of dynamical systems with several degrees of freedom (Russian, English), Dokl. Akad. Nauk SSSR 156 (1964) 9-12.
3. J. Ball & V. Mizel, One dimensional variational problems whose minimizers do not satisfy the Euler-Lagrange equation, Arch. Ration. Mech. Anal. 90 (1985) 325-388.
4. V. Bangert, Geodesic rays, Busemann functions and monotone twist maps, Calc. Var. Partial Differ. Equ. 2(1) (1994) 49-63.
5. P. Bernard, Connecting orbits of time dependent Lagrangian systems, Ann. Inst. Fourier (Grenoble) 52(5) (2002) 1533-1568.
6. U. Bessi, An approach to Arnold’s diffusion through the calculus of variations, Nonlinear Anal. 26(6) (1996) 1115-1135.
7. U. Bessi, L. Chierchia & E. Valdinoci, Upper bounds on Arnold diffusion times via Mather theory, J. Math. Pures Appl. 80(1) (2001) 105-129.
8. S. Bolotin, Homoclinic orbits in invariant tori of Hamiltonian systems, Dynamical systems in classical mechanics, 21-90, Amer. Math. Soc. Transl. Ser. 2, 168, Amer. Math. Soc., Providence, RI, 1995.
9. A. Delshams, R. de la Llave & T.M. Seara, A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: announcement of results, Electron. Res. Announc. Amer. Math. Soc. 9 (2003) 125-134 (electronic).
10. A. Delshams, R. de la Llave & T.M. Seara, Geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: heuristic and rigorous verification of a model, preprint, 2003.
11. A. Fathi & J. Mather, Failure of convergence of the Lax-Oleinik semi-group in the time-periodic case, Bull. Soc. Math. France 128(3) (2000) 473-483.
12. M.W. Hirsch, C.C. Pugh & M. Shub, Invariant manifolds, Lecture Notes in Mathematics, 583, Springer-Verlag, Berlin-New York, 1977.
13. J. Mather, Existence of quasiperiodic orbits for twist homeomorphisms of the annulus, Topology 21(4) (1982) 457-467.
14. J. Mather, Action minimizing invariant measures for positive definite Lagrangian systems, Math. Z. 207(2) (1991) 169-207.
15. J. Mather, Variational construction of connecting orbits, Ann. Inst. Fourier (Grenoble) 43(5) (1993) 1349-1386.
16. J. Mather, Arnold diffusion, I: Announcement of results, preprint, 2002.
17. J.K. Moser, On the volume elements on a manifold, Trans. Amer. Math. Soc. 120 (1965) 286-294.
18. H. Rademacher, Uber partielle und totale Differenzierbarkeit von Funktionen mehrerer Variabeln und Uber die Transformation der Doppelintegrale, Math. Ann. 79 (1919) 340-359.
19. A. Weinstein, Symplectic manifolds and their Lagrangian submanifolds, Advances in Math. 6 (1971) 329-346.
20. Z. Xia, Arnold diffusion: a variational construction, Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998), Doc. Math. 1998, Extra Vol. 2, 867-877 (electronic).