@article{AIHPA_1995__63_2_125_0,
author = {Moszy\'nski, Marcin},
title = {On classical intrinsically resonant formal perturbation theory},
journal = {Annales de l'I.H.P. Physique th\'eorique},
volume = {63},
year = {1995},
pages = {125-154},
mrnumber = {1357493},
zbl = {0832.70016},
language = {en},
url = {http://dml.mathdoc.fr/item/AIHPA_1995__63_2_125_0}
}
Moszyński, Marcin. On classical intrinsically resonant formal perturbation theory. Annales de l'I.H.P. Physique théorique, Tome 63 (1995) pp. 125-154. http://gdmltest.u-ga.fr/item/AIHPA_1995__63_2_125_0/
[1] , Mathematical Methods of Classical Mechanics, Moscow, Nauka, 1974 (in Russian). | MR 474390
[2] , , and , A proof of Kolmogorov's theorem on invariant tori using canonical transformations defined by the Lie method, Il Nuovo Cimento, Vol. 79 B, No. 2, 1984, pp. 201-223. | MR 743977
[3] and , Stability of motion near resonances in quasi integrable hamiltonian systems, Journal of Statistical Physics, Vol. 44, 1986, pp. 293-338. | MR 857061 | Zbl 0636.70018
[4] , and , Quantization of the classical Lie algorithm in the Bargman representation, Annals of Physics, Vol. 209, 1991, pp. 364-392. | MR 1117300 | Zbl 0875.47008
[5] , Lie series method for vector fields and hamiltonian perturbation theory, Journal of Applied Mathematics and Physics (ZAMP), Vol. 41, 1990, pp. 843-864. | MR 1082741 | Zbl 0746.70012
[6] and , Stochastic behaviour of resonant nearly linear oscillator systems in the limit of zero nonlinear coupling, Physical Review, Vol. 1 A, 1970, pp. 59-70.
[7] , The Elements of Mechanics, New York, Springer, 1983. | MR 698947 | Zbl 0512.70001
[8] and , Rigorous estimates for the series expansions of hamiltonian perturbation theory, Celestial Mechanics, Vol. 37, 1985, pp. 95-112. | MR 838181
[9] , A note on uniqueness of the normal form for quasi-integrable systems, Meccanica, Vol. 27, 1992, pp. 281-284. | Zbl 0768.58043
[10] and , Resonant modification and destruction of adiabatic invariants, Annals of Physics, Vol. 71, 1972, pp. 319-356.
[11] , Calcul formel pour les méthodes de Lie en mécanique hamiltonienne, Thèse, École Polytechnique, Paris, 1993.
[12] and , Regular and Stochastic Motion, Berlin, Springer, 1983. | MR 681862 | Zbl 0506.70016
[13] , Canonical perturbation theory via simultaneous approximation, Russian Mathematical Surveys, Vol. 47:6, 1992, pp. 57-133. | MR 1209145 | Zbl 0795.58042
[14] , Stability of hamiltonian systems over exponentially long times. The nearlinear case, Proceedings of the Cincinnati 1992 Conference on Hamiltonian Dynamical Systems, IMA Publ. | Zbl 0836.58025
[15] and , Invariants of nearly periodic hamiltonian systems, Culham Laboratory Report, CLM P111, 1966, Culham England. | Zbl 0176.23003
[16] , Les Méthodes Nouvelles de la Mécanique Céleste, Vol. 1, Paris, Gauthier-Villars, 1897. | JFM 24.1130.01
[17] , Nekhoroshev estimates for quasiconvex hamiltonian systems, Mathematishe Zeitschrift, Vol. 213, 1993, pp. 187-216. | MR 1221713 | Zbl 0857.70009
[18] , A Nekhoroshev-like theory of classical particle channeling in perfect crystals, Dynamics Reported, Expositions in Dynamical Systems, New Series, Vol. 2, 1993, pp. 69-115. | MR 1347925 | Zbl 0795.70010