Berti, Massimiliano and Bolle, Philippe:
Diffusion time and splitting of separatrices for nearly integrable isochronous Hamiltonian systems (Tempo di diffusione e splitting delle separatrici per sistemi Hamiltoniani isocroni quasi-integrabili)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni Serie 9 11 (2000), fasc. n.4, p. 235-243, (English)
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Sunto
Consideriamo il problema della diffusione di Arnold per sistemi Hamiltoniani isocroni quasi-integrabili. Dimostriamo un teorema di shadowing che migliora le stime sul tempo di diffusione sinora note. Giustifichiamo inoltre, per sistemi a tre scale temporali, che lo splitting delle separatrici è correttamente previsto dalla funzione di Poincaré-Melnikov.
Referenze Bibliografiche
[2]
S. Angenent,
A variational interpretation of Melnikov’s function and exponentially small separatrix splitting. In:
D.A. Salamon (ed.),
Symplectic geometry.
London Math. Soc., Lecture Notes Series, vol.
192,
Cambridge University Press 1993. |
MR 1297127 |
Zbl 0810.34037[3]
V.I. Arnold,
Instability of dynamical systems with several degrees of freedom.
Sov. Math. Dokl.,
6,
1964, 581-585. |
Zbl 0135.42602[4]
M. Berti -
P. Bolle,
Homoclinics and Chaotic Behaviour for Perturbed Second order Systems.
Annali di Mat. Pura e Applicata, (IV), vol.
CLXXVI,
1999, 323-378. |
fulltext (doi) |
MR 1746547 |
Zbl 0957.37019[6]
M. Berti -
P. Bolle,
Arnold’s diffusion for nearly integrable isochronous Hamiltonian systems. Preprint SISSA 98/2000/M, october
2000. |
fulltext mini-dml |
MR 1837581[7]
U. Bessi -
L. Chierchia -
E. Valdinoci,
Upper Bounds on Arnold Diffusion Time via Mather theory.
Journal de Mathématiques Pures et Appliquées, neuvième série, to appear. |
fulltext (doi) |
MR 1810511 |
Zbl 0986.37052[9] J. Cresson, Conjecture de Chirikov et Optimalité des exposants de stabilité du théorème de Nekhoroshev. Dép. de Mathématiques de Besançon, 1998, preprint.
[10]
A. Delshams -
V.G. Gelfreich -
V. G. Jorba -
T. M. Seara,
Exponentially small splitting of separatrices under fast quasi-periodic forcing.
Comm. Math. Ph.,
189,
1997, 35-71. |
fulltext (doi) |
MR 1478530 |
Zbl 0897.34042[12]
G. Gallavotti -
G. Gentile -
V. Mastropietro,
Separatrix splitting for systems with three time scales.
Commun. Math. Phys.,
202,
1999, 197-236. |
fulltext (doi) |
MR 1686531 |
Zbl 0936.37034[14]
P. Lochak,
Arnold diffusion: a compendium of remarks and questions.
Proceedings of 3DHAM’s Agaro,
1995. |
Zbl 0986.37054[15]
P. Lochak -
J.P. Marco -
D. Sauzin,
On the splitting of invariant manifolds in multidimensional Hamiltonian systems. Université Jussieu, preprint. |
Zbl 1038.70001[17] A. Pumarino - C. Valls, Three time scales systems exhibiting persisent Arnold’s diffusion. Preprint; www.ma.utexas.edu/mp arc.