Rigorous numerical stability estimates for the existence of KAM tori in a forced pendulum
Annales de l'I.H.P. Physique théorique, Tome 47 (1987) no. 1, pp. 85-111. 
@article{AIHPA_1987__47_1_85_0,
     author = {Celletti, Alessandra and Falcolini, Corrado and Porzio, Anna},
     title = {Rigorous numerical stability estimates for the existence of {KAM} tori in a forced pendulum},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {85--111},
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     number = {1},
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     mrnumber = {912758},
     zbl = {0636.70017},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPA_1987__47_1_85_0/}
}
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Celletti, Alessandra; Falcolini, Corrado; Porzio, Anna. Rigorous numerical stability estimates for the existence of KAM tori in a forced pendulum. Annales de l'I.H.P. Physique théorique, Tome 47 (1987) no. 1, pp. 85-111. http://archive.numdam.org/item/AIHPA_1987__47_1_85_0/

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

[2] G. Gallavotti, Perturbation theory for classical hamiltonian systems, « Scaling and Self Similarity », Progress in Physics, t. 7, 1984. | MR

[3] G. Gallavotti, Quasi integrable mechanical systems, Les Houches Summer School 1984, procendings, ed. K. Osterwalder, R. Stora, North Holland, 1986 (in print). | MR | Zbl

[4] G. Inglese, Thesis. Stime di stabilità in presenza di piccoll denominatori nel caso di sistemi hamiltoniani unidimensionali non autonomi, Roma, 1980.

[5] A. Porzio, Stability bounds for the existence of KAM tori in a forced pendulum, in print: Boll. Unione Matematica Italiana, 1986. | MR | Zbl

[6] A. Celletti, C. Falcolini, A. Porzio, Rigorous KAM stability statements for non autonomous one-dimensional hamiltonian systems, 1986. | Zbl

[7] D. Escande, F. Doveil, Renormalization method for computing the threshold of the large scale stochasticity in two degrees of freedom hamiltonian systems. Journ. Stat. Phys., t. 26, 1981, p. 2. | MR

[8] G.H. Hardy, E.M. Wright, The theory of numbers, Oxford, 1979. | Zbl

[9] M. Hénon, C. Heiles, The applicability of the third integral of motion: some numerical experiments. Astr. Journ., t. 69, 1964, p. 1. | MR

[10] M. Hénon, Exploration numérique du problème restreint. Ann. d'Astroph., t. 28, 1965, p. 3. | Zbl

[11] G. Benettin, M. Casartelli, L. Galgani, A. Giorgilli, J.M. Strelcyn, Nuovo Cimento, t. 50 B, 1979, p. 211. | MR

[12] B. Chirikov, Phys. Rep., t. 52, 1979.

[13] J. Greene, Journ. of Math. Phys., t. 20, 1979.

[14] C. Liverani, G. Servizi, G. Turchetti, Lettere al Nuovo Cimento, t. 39, 1984, p. 417. | MR

[15] C. Liverani, G. Turchetti, Improved KAM estimates for the Siegel radius, 1985. | MR | Zbl

[16] A. Celletti, L. Chierchia, Rigorous Estimates for a Computer-Assisted KAM theory, to appear in J. of Math. Phys. | MR | Zbl

[17] Vax-11 Fortran IV, Plus, Language reference manual, Digital Equipment Corporation, Maynard, Massachusetts, 1978.

[18] G. Benettin, L. Galgani, A. Giorgilli, Classical perturbation theory for systems of weakly coupled rotators, 1984. | MR

[19] Vax-11 Fortran IV, Plus, User's Guide, Digital Equipment Corporation, Maynard, Massachusetts, 1978.

[20] Vax-11 Fortran IV, Plus, Run-time library reference manual, Digital Equipment Corporation, Maynard, Massachusetts, 1978.

[21] D. Escande, private communication.