Drift and diffusion in phase space

 Access to full text

 Full (PDF)

1. [A] V. Arnold, Instability of Dynamical Systems with Several Degrees of Freedom, Sov. Mathematical Dokl., Vol. 5, 1966, pp. 581-585. 
2. [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. Zbl0872.58054MR1158353
3. [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. Zbl0636.70018MR857061
4. [CG] L. Chierchia and G. Gallavotti, Smooth Prime Integrals for Quasi-Integrable Hamiltonian Systems II, Nuovo Cimento, Vol. 67B, 1982, pp. 277-295. MR657905
5. [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. Zbl0695.34040
6. [D] R. Douady, Stabilité ou instabilité des points fixes elliptiques, Annales Scientifiques de l'École Normale Supérieure, Vol. 21, 1988, pp. 1-46. Zbl0656.58020MR944100
7. [DS] A. Delshams and M.T. Seara, An Asymptotic Expression for the Splitting of Separatrices of Rapidly Forced Pendulum, preprint, 1991. 
8. [G] G. Gallavotti, The Elements of Mechanics, Springer, 1983. Zbl0512.70001MR698947
9. [Ge] V.G. Gelfreich, Separatrices Splitting for the Rapidly Forced Pendulum, preprint, 1992. MR1279388
10. [GLT] V.G. Gelfreich, V.F. Lazutkin and M.B. Tabanov, Exponentially Small Splitting in Hamiltonian Systems, Chaos, Vol. 1, (2), 1991. Zbl0899.58016MR1135901
11. [Gr] S.M. Graff, On the Conservation for Hyperbolic Invariant Tori for Hamiltonian Systems, J. Differential Equations, Vol. 15, 1974, pp. 1-69. Zbl0257.34048MR365626
12. [HMS] P. Holmes, J. Marsden and J. Scheurle, Exponentially Small Splittings of Separatrices in KAM Theory and Degenerate Bifurcations, preprint, 1989. Zbl0685.70017
13. [L] S. De La Place, Mécanique Céleste, tome II, livre 5, ch. I, 1799, English Translation by E. Bodwitch, reprinted by Chelsea, 1966. 
14. [La1] V.F. Lazutkin, The Existence of Caustics for a Billiard Problem in a Convex Domain, Izv. Akad. Nauk. SSSR, Vol. 37, (1), 1973. Zbl0277.52002
15. [La2] V.F. Lazutkin, Separatrices Splitting for Standard and Semistandard Mappings, preprint, 1989. 
16. [LW] R. De La Llave, E. Wayne, Whiskered Tori, preprint, 1990. 
17. [M] J. Moser, Convergent Series Expansions for Quasi-Periodic Motions, Matematische Annalen, Vol. 169, 1967, pp. 136-176. Zbl0179.41102MR208078
18. [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. Zbl0135.31001MR156048
19. [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. Zbl0389.70028
20. [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. Zbl0571.70022MR802878
21. [P] H. Poincaré, Les Méthodes nouvelles de la mécanique céleste, 1892, reprinted by Blanchard, Paris, 1987. Zbl0651.70002
22. [Pö] J. Pöschel, Integrability of Hamiltonian Systems on Cantor Sets, Communications Pure Appl. Math., Vol. 35, 1982, pp. 653-696. Zbl0542.58015MR668410
23. [Sv] N.V. Svanidze, Small Perturbations of an Integrable Dynamical System with an Integral Invariant, Proceed. Steklov Institute of Math., Vol. 2, 1981. Zbl0463.58016MR573904
24. [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. Zbl0309.58006MR380867

1. Luca Biasco, Luigi Chierchia, Nekhoroshev stability for the D’Alembert problem of Celestial Mechanics
2. Giovanni M. Gallavotti, Reminiscences on science at IHÉS. A problem on homoclinic theory and a brief review
3. Jean-Pierre Marco, Transition le long des chaînes de tores invariants pour les systèmes hamiltoniens analytiques
4. L. Chierchia, C. Falcolini, A direct proof of a theorem by Kolmogorov in hamiltonian systems
5. Massimiliano Berti, Philippe Bolle, Diffusion time and splitting of separatrices for nearly integrable isochronous Hamiltonian systems
6. Massimiliano Berti, Luca Biasco, Philippe Bolle, Optimal stability and instability results for a class of nearly integrable Hamiltonian systems
7. Massimiliano Berti, Philippe Bolle, A functional analysis approach to Arnold diffusion