On classical intrinsically resonant formal perturbation theory
Annales de l'I.H.P. Physique théorique, Tome 63 (1995) no. 2, pp. 125-154. 
@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/}
}
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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] W.I. Arnold, Mathematical Methods of Classical Mechanics, Moscow, Nauka, 1974 (in Russian). | MR

[2] G. Benerfin, L. Galgani, A. Giorgilli and J.-M. Strelcyn, 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

[3] G. Benettin and G. Gallavotti, Stability of motion near resonances in quasi integrable hamiltonian systems, Journal of Statistical Physics, Vol. 44, 1986, pp. 293-338. | MR | Zbl

[4] M. Degli Esposti, S. Graffi and J. Herczyński, Quantization of the classical Lie algorithm in the Bargman representation, Annals of Physics, Vol. 209, 1991, pp. 364-392. | MR | Zbl

[5] F. Fassó, 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] J. Ford and G.H. Lunsford, 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] G. Galavotti, The Elements of Mechanics, New York, Springer, 1983. | MR | Zbl

[8] A. Giorgilli and L. Galgani, Rigorous estimates for the series expansions of hamiltonian perturbation theory, Celestial Mechanics, Vol. 37, 1985, pp. 95-112. | MR

[9] J. Herczyński, A note on uniqueness of the normal form for quasi-integrable systems, Meccanica, Vol. 27, 1992, pp. 281-284. | Zbl

[10] E.F. Jager and A.L. Lichtenberg, Resonant modification and destruction of adiabatic invariants, Annals of Physics, Vol. 71, 1972, pp. 319-356.

[11] P.V. Koseleff, Calcul formel pour les méthodes de Lie en mécanique hamiltonienne, Thèse, École Polytechnique, Paris, 1993.

[12] A.J. Lichtenberg and M.A. Lieberman, Regular and Stochastic Motion, Berlin, Springer, 1983. | MR | Zbl

[13] P. Lochak, Canonical perturbation theory via simultaneous approximation, Russian Mathematical Surveys, Vol. 47:6, 1992, pp. 57-133. | MR | Zbl

[14] P. Lochak, 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] B. Mcnamara and R.I. Whiteman, Invariants of nearly periodic hamiltonian systems, Culham Laboratory Report, CLM P111, 1966, Culham England. | Zbl

[16] H. Poincaré, Les Méthodes Nouvelles de la Mécanique Céleste, Vol. 1, Paris, Gauthier-Villars, 1897. | JFM

[17] J. Pöschel, Nekhoroshev estimates for quasiconvex hamiltonian systems, Mathematishe Zeitschrift, Vol. 213, 1993, pp. 187-216. | EuDML | MR | Zbl

[18] H. Scott Dumas, 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