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Converse KAM theory for monotone positive symplectomorphisms

Àlex Haro

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Recommended by A I Neishtadt

We apply variational methods to converse KAM theory. These are useful for symplectomorphisms in the annulus that satisfy weaker hypotheses than those usually required. For instance, we do not need the existence of a global Lagrangian generating function. We obtain the variational principles from the primitive function of our symplectomorphism. They are introduced not only for the orbits of a symplectomorphism, but also for the so-called invariant Lagrangian graphs (ILG). Among the non-degenerate ILG we focus on the minimizing ones. Applications are also described for a broad class of examples.


PACS

45.10.Db Variational and optimization methods

45.20.Jj Lagrangian and Hamiltonian mechanics

MSC

70H30 Other variational principles

37J40 Perturbations, normal forms, small divisors, KAM theory, Arnol'd diffusion

70H08 Nearly integrable Hamiltonian systems, KAM theory

Subjects

Mathematical physics

Computational physics

Dates

Issue 5 (September 1999)

Received 26 October 1998



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