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A possible mechanism for the KAM tori breakdown. (English) Zbl 0958.37036

Simó, Carles (ed.), Hamiltonian systems with three or more degrees of freedom. Proceedings of the NATO Advanced Study Institute, S’Agaró, Spain, June 19-30, 1995. Dordrecht: Kluwer Academic Publishers. NATO ASI Ser., Ser. C, Math. Phys. Sci. 533, 372-376 (1999).
Summary: Inspired by the quantum field theory, a resummation is performed in the Lindstedt series defining the KAM tori, and a possible mechanism for universality of the tori breakdown is discussed. This work is mostly based on a joint paper with G. Gallavotti [Math. Phys. Electron. J. 1, No. 5, 13 p. (1995; Zbl 0849.58038)].
For the entire collection see [Zbl 0942.00030].

MSC:

37J40 Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion
70H08 Nearly integrable Hamiltonian systems, KAM theory
37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)

Citations:

Zbl 0849.58038
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