Nekhoroshev estimate for isochronous non resonant symplectic maps

Springer Science and Business Media LLC - Tập 47 Số 4 - Trang 333-359 - 1990
Armando Bazzani1, Stefano Marmi1, G. Turchetti1
1Dipartimento di Fisica, Universitd di Bologna INFN-Sezione di Bologna, Via Irnerio 46, I-40126, Bologna, Italy

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Kolmogorov, A.N.: 1954, Dokl. Akad. Nauk SSSR, 98, 527?530.

Arnol'd, V.I.: 1963, Russ. Math. Surv., 18, 9?36, and 85?191.

Moser, J.: 1962, Nachr. Akad. Wiss. Göttingen, Math.-Phys. Kl. 1, 1.

Arnol'd, V.I.: 1964, Sov. Math. Dokl., 5, 581?585.

Nekhoroshev, N.N.: 1977, Russ. Math. Surv., 32, 1?65.

Littlewood, J.E.: 1959, Proc. London Math. Soc., 9, 343?372.

Benettin, G.: 1988, ?Nekhoroshev-like results for Hamiltonian Dynamcal Systems?. In Nonlinear Evolution and Chaotic Phenomena (G. Gallavotti and P.F Zweifel editors), Plenum Press, New York.

Gallavotti, G.: 1984, ?Quasi-Integrable Mechanical Systems?. In Critical Phenomena, Random Systems, Gauge Theories (K. Osterwalder and R. Stora editors), Les Houches, Session XLIII, North Holland, Amsterdam.

Giorgilli, A. and Galgani, L.: 1985, Cel. Mech., 37, 95?112.

Benettin, G. and Gallavotti, G.: 1986, J. Stat. Phys., 44, 293?338.

Giorgilli, A., Delshams, A., Fontich, E., Galgani L. and Simò, C.: 1989, ?Effective Stability for a Hamiltonian System near an Elliptic Equilibrium Point, with an Application to the Restricted Three-Body Problem?. J. Dif. Eq., 77, 167?198.

Palis, J. and Yoccoz, J.C. : 1988, ?Rigidity of Centalizers of Diffeomorphisms.? Ann. Ec. Norm. Sup., in press.

Roels, J. and Henon, M.: 1967, Bull. Astr. (Ser. 3), 2, 267?285.

Rannou, F.: 1974, Astron. and Astrophys., 31, 289?301.

Wisdom, J.: 1982, Astron. J., 87, 577.

Wisdom, J.: 1983, Icarus, 56, 51.

Herrera, J.C. : 1979, ?Nonlinear Dynamics and the beam-beam interaction.? Am. Inst. of Phys., 232.

Dragt, A.J. :1982, ?Lectures in nonlinear orbit dynamics.? In A.I.P. Conf. Proc., 87.

Dragt, A.J. : 1986, Nonlinear Dynamics and particle accelerators, Lecture Notes in Physics, 247.

Bazzani, A., Mazzanti, P., Servizi, G. and Turchetti, G.: 1988, Nuovo Cimento, 102B, 51?80.

Bazzani, A., Leemann, T., Scandale, W., Servizi, G. and Turchetti, G. : 1989, ?Description of nonlinear beam dynamics in the CERN large hadron collider by using normal form algorithms.? In EPAC Conference proceedings (S. Tazzari Ed.), World Scientific.

Liechtenberg, A. J. and Lieberman, M. A. : 1983, Regular and stochastic motion, Chap 6, Springer Verlag.

Ortolani, A. :1987, ?Physics of mirrors, reversed field pinches and compact tori.? International School of Plasma Physics. Ed. Compositori.

Bazzani, A. and Turchetti, G.: 1989, ?Analisi di superfici magnetiche in geometria toroidale?. Atti Sem. Mat. Fis. Un. Modena, XXXVII, 157.

Bazzani, A., Malavasi, M., Siboni, S. and Turchetti, G. : 1989, ?Perturbative methods in the analysis of magnetic fields structure.? Dip. di Fisica della Università di Bologna, preprint.

Birkhoff, G.D.: 1920, Acta Math., 43, 1?119.

Bazzani, A.: 1988, ?Normal Forms for symplectic maps in R 2n?. Cel. Mech., 42, 107?128.

Moser, J.: 1956, Comm. Pure Appl. Math., 9, 673?692.

Servizi, G., Turchetti, G., Benettin, G. and Giorgilli, A.: 1983, Phys. Lett., A95, 11.

Servizi, G. and Turchetti, G.: 1986, Nuovo Cimento, B95, 121.

Turchetti, G.: 1988, ?Perturbative Methods for Hamiltonian Maps?. In Methods and Applications of Nonlinear Dynamics (A.W. Sáenz Ed.), 95?154, World Scientific, Singapore.

Malavasi, M., Marmi, S., Servizi, G. and Turchetti, G. : 1990, in preparation.

Bessis, D., Marmi, S. and Turchetti, G. : 1989, ?On the Singularities of Divergent Majorant Series arising from Normal Form Theory.? Rendiconti di Matematica, to appear.

Meyer, K.R.: 1974, ?The Implicit Function Theorem and Analytic Differential Equations?. Lect. Notes in Math., 468, 191?208.

Liverani, C. and Turchetti, G.: 1986, J. Stat. Phys., 45, 1071?1086.

Marmi, S.: 1988, Meccanica, 23, 139?146.