Arnold's example with three rotators

Nonlinearity

Volumn 10, Issue 3, 1997, Pages 763-781

  Bessi, Ugo ^a  

^a SCUOLA NORMALE SUPERIORE   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001602480     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/10/3/010     Document Type: Article

References (20)

1. Arnold V I 1964 Instability of dynamical systems with several degrees of freedom Sov. Math. 5 581-5
2. Bernard P 1996 Perturbation d'un Hamiltonien partiellement hyperbolique C. R. Acad. Sci., Paris 323 189-94
3. Bernstein D and Katok A 1987 Birkhoff periodic orbits for small perturbations of completely integrable Hamiltonian systems with convex Hamiltonians Inv. Math. 88 225-41
4. Bessi U 1996 An approach to Arnold's diffusion through the calculus of variations Nonlinear Anal. TMA 26 1115-35
5. Chierchia L and Gallavotti G 1994 Drift and diffusion in Hamiltonian systems Ann. Inst. H. Poincaré, Phys. Theorique 60 1-144
6. Coti Zelati V and Rabinowitz P H 1991 Homoclinic orbits for second order Hamiltonian systems possessing superquadratic potentials J. Am. Math. Soc. 4 693-727
7. Easton R W 1981 Orbit structure near trajectories biasymptotic to invariant tori, Devaney-Nitecki Classical Mechanics and Dynamical Systems pp 55-67
8. Easton R W 1978 Homoclinic phenomena in Hamiltonian systems with several degrees of freedom J. Diff. Eqns 29 241-52
9. Hardy G H and Wright E M 1938 An Introduction to the Theory of Numbers (Oxford: Clarendon)
10. Holmes P J and Marsden J E 1982 Melnikov's method and Arnold diffusion for perturbations of integrable Hamiltonian systems J. Math. Phys. 23 669-75
11. Lochak P 1993 Hamiltonian perturbation theory: periodic ordits, resonances and intermittency Nonlinearity 6 885-904
12. Lochak P 1995 Arnold's diffusion, a compendium of remarks and questions Proc. 3DHAM (s'Agaro) (Dordrecht: Kluwer Academic) to appear
13. Lochak P 1992 Canonical perturbation theory via simultaneous approximation Russ. Math. Surv 47 57-134
14. Lochak P and Nishtadt A I 1992 Estimates in the theorem of N N Nekhorocheff for systems with a quasi-convex Hamiltonian Chaos 2 495-9
15. Marco J-P 1997 Transition le long des chaines de tores invariants pour les systémes Hamiltoniens analytiques Ann. Inst. H. Poincaré to appear
16. Mather J N 1993 Variational construction of connecting orbits Ann. Inst. Fourier 43 1349-68
17. Nekhorocheff N N 1977 An exponential estimate on the time of stability of nearly-integrable Hamiltonian systems Russ. Math. Surv. 32 1-65
18. Poeschel J 1993 Nekhorocheff estimates for quasi-convex Hamiltonian systems Z. Math. 213 187-216
19. Rudnev M and Wiggins S 1997 Existence of exponentially small separatrix splittings and homoclinic and heteroclinic connections between whiskered tori in weakly hyperbolic near-integrable Hamiltonian systems Preprint
20. Séré E 1993 Looking for the Bernoulli shift Ann. Inst. H. Poincaré, Anal. non Linéaire 10 561-90