Drift and diffusion in phase space
Chierchia, L. ; Gallavotti, G.
Annales de l'I.H.P. Physique théorique, Tome 61 (1994), p. 1-144 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPA_1994__60_1_1_0,
     author = {Chierchia, Luigi and Gallavotti, Giovanni M.},
     title = {Drift and diffusion in phase space},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {61},
     year = {1994},
     pages = {1-144},
     mrnumber = {1259103},
     zbl = {1010.37039},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1994__60_1_1_0}
}

Chierchia, L.; Gallavotti, G. Drift and diffusion in phase space. Annales de l'I.H.P. Physique théorique, Tome 61 (1994) pp. 1-144. http://gdmltest.u-ga.fr/item/AIHPA_1994__60_1_1_0/

[A] V. Arnold, Instability of Dynamical Systems with Several Degrees of Freedom, Sov. Mathematical Dokl., Vol. 5, 1966, pp. 581-585.

[ACKR] C. Amick, E.S.C. Ching, L.P. Kadanoff and V. Rom-Kedar, Beyond All Orders: Singular Perturbations in a Mapping, J. Nonlinear Sci., Vol. 2, 1992, pp. 9-67. | MR 1158353 | Zbl 0872.58054

[BG] G. Benetrin and G. Gallavotti, Stability of Motions Near Resonances in Quasi-Integrable Hamiltonian Systems, J. Statistical Physics, Vol. 44, 1986, pp. 293-338. | MR 857061 | Zbl 0636.70018

[CG] L. Chierchia and G. Gallavotti, Smooth Prime Integrals for Quasi-Integrable Hamiltonian Systems II, Nuovo Cimento, Vol. 67B, 1982, pp. 277-295. | MR 657905

[CZ] L. Chierchia and E. Zehnder, Asymptotic Expansions of Quasi-Periodic Motions, Annali della Scuola Normale Superiore di Pisa, Serie IV, Vol. XVI, Fasc. 2, 1989. | Numdam | Zbl 0695.34040

[D] R. Douady, Stabilité ou instabilité des points fixes elliptiques, Annales Scientifiques de l'École Normale Supérieure, Vol. 21, 1988, pp. 1-46. | Numdam | MR 944100 | Zbl 0656.58020

[DS] A. Delshams and M.T. Seara, An Asymptotic Expression for the Splitting of Separatrices of Rapidly Forced Pendulum, preprint, 1991.

[G] G. Gallavotti, The Elements of Mechanics, Springer, 1983. | MR 698947

[Ge] V.G. Gelfreich, Separatrices Splitting for the Rapidly Forced Pendulum, preprint, 1992. | MR 1279388

[GLT] V.G. Gelfreich, V.F. Lazutkin and M.B. Tabanov, Exponentially Small Splitting in Hamiltonian Systems, Chaos, Vol. 1, (2), 1991. | MR 1135901 | Zbl 0899.58016

[Gr] S.M. Graff, On the Conservation for Hyperbolic Invariant Tori for Hamiltonian Systems, J. Differential Equations, Vol. 15, 1974, pp. 1-69. | MR 365626 | Zbl 0257.34048

[HMS] P. Holmes, J. Marsden and J. Scheurle, Exponentially Small Splittings of Separatrices in KAM Theory and Degenerate Bifurcations, preprint, 1989.

[L] S. De La Place, Mécanique Céleste, tome II, livre 5, ch. I, 1799, English Translation by E. Bodwitch, reprinted by Chelsea, 1966.

[La1] V.F. Lazutkin, The Existence of Caustics for a Billiard Problem in a Convex Domain, Izv. Akad. Nauk. SSSR, Vol. 37, (1), 1973. | Zbl 0277.52002

[La2] V.F. Lazutkin, Separatrices Splitting for Standard and Semistandard Mappings, preprint, 1989.

[LW] R. De La Llave, E. Wayne, Whiskered Tori, preprint, 1990.

[M] J. Moser, Convergent Series Expansions for Quasi-Periodic Motions, Matematische Annalen, Vol. 169, 1967, pp. 136-176. | MR 208078 | Zbl 0179.41102

[Me] V.K. Melnikov, On the Stability of the Center for Time Periodic Perturbations, Trans. Moscow Math. Math. Soc., Vol. 12, 1963, pp. 1-57. | MR 156048 | Zbl 0135.31001

[N] N. Nekhorossev, An Exponential Estimate of the Time of Stability of Nearly Integrable Hamiltonian Systems, Russian Mathematical Surveys, Vol. 32, 1975, pp. 1-65. | Zbl 0389.70028

[Nei] A.I. Neihstad, The Separation of Motions in Systems with Rapidly Rotating Phase, PMM U.S.S.R., Vol. 48, 1984, pp. 133-139. | MR 802878 | Zbl 0571.70022

[P] H. Poincaré, Les Méthodes nouvelles de la mécanique céleste, 1892, reprinted by Blanchard, Paris, 1987.

[Pö] J. Pöschel, Integrability of Hamiltonian Systems on Cantor Sets, Communications Pure Appl. Math., Vol. 35, 1982, pp. 653-696. | MR 668410 | Zbl 0542.58015

[Sv] N.V. Svanidze, Small Perturbations of an Integrable Dynamical System with an Integral Invariant, Proceed. Steklov Institute of Math., Vol. 2, 1981. | MR 573904 | Zbl 0463.58016

[Z] E. Zehnder, Generalized Implicit Function Theorems with Applications to some Small Divisor Problems I, II, Communications Pure Applied Mathematics, Vol. 28, 1975, pp. 91-140. | MR 380867 | Zbl 0309.58006