@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}, pages = {125--154}, publisher = {Gauthier-Villars}, volume = {63}, number = {2}, year = {1995}, mrnumber = {1357493}, zbl = {0832.70016}, language = {en}, url = {http://www.numdam.org/item/AIHPA_1995__63_2_125_0/} }
TY - JOUR AU - Moszyński, Marcin TI - On classical intrinsically resonant formal perturbation theory JO - Annales de l'I.H.P. Physique théorique PY - 1995 SP - 125 EP - 154 VL - 63 IS - 2 PB - Gauthier-Villars UR - http://www.numdam.org/item/AIHPA_1995__63_2_125_0/ LA - en ID - AIHPA_1995__63_2_125_0 ER -
Moszyński, Marcin. On classical intrinsically resonant formal perturbation theory. Annales de l'I.H.P. Physique théorique, Tome 63 (1995) no. 2, pp. 125-154. http://www.numdam.org/item/AIHPA_1995__63_2_125_0/
[1] Mathematical Methods of Classical Mechanics, Moscow, Nauka, 1974 (in Russian). | MR
,[2] 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
, , and ,[3] Stability of motion near resonances in quasi integrable hamiltonian systems, Journal of Statistical Physics, Vol. 44, 1986, pp. 293-338. | MR | Zbl
and ,[4] Quantization of the classical Lie algorithm in the Bargman representation, Annals of Physics, Vol. 209, 1991, pp. 364-392. | MR | Zbl
, and ,[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 | Zbl
,[6] Stochastic behaviour of resonant nearly linear oscillator systems in the limit of zero nonlinear coupling, Physical Review, Vol. 1 A, 1970, pp. 59-70.
and ,[7] The Elements of Mechanics, New York, Springer, 1983. | MR | Zbl
,[8] Rigorous estimates for the series expansions of hamiltonian perturbation theory, Celestial Mechanics, Vol. 37, 1985, pp. 95-112. | MR
and ,[9] A note on uniqueness of the normal form for quasi-integrable systems, Meccanica, Vol. 27, 1992, pp. 281-284. | Zbl
,[10] Resonant modification and destruction of adiabatic invariants, Annals of Physics, Vol. 71, 1972, pp. 319-356.
and ,[11] Calcul formel pour les méthodes de Lie en mécanique hamiltonienne, Thèse, École Polytechnique, Paris, 1993.
,[12] Regular and Stochastic Motion, Berlin, Springer, 1983. | MR | Zbl
and ,[13] Canonical perturbation theory via simultaneous approximation, Russian Mathematical Surveys, Vol. 47:6, 1992, pp. 57-133. | MR | Zbl
,[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
,[15] Invariants of nearly periodic hamiltonian systems, Culham Laboratory Report, CLM P111, 1966, Culham England. | Zbl
and ,[16] Les Méthodes Nouvelles de la Mécanique Céleste, Vol. 1, Paris, Gauthier-Villars, 1897. | JFM
,[17] Nekhoroshev estimates for quasiconvex hamiltonian systems, Mathematishe Zeitschrift, Vol. 213, 1993, pp. 187-216. | EuDML | MR | Zbl
,[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 | Zbl
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