99-101 Alex Haro

Converse KAM theory for monotone positive symplectomorphisms (2793K, gzipped ps) Apr 8, 99

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Abstract. We apply variational methods to Converse KAM theory, being useful for symplectomorphisms in the annulus satisfying weaker hypothesis that usually one requires. For instance, we do not need the existence of a global Lagrangian generating function. The main object is the primitive function of an exact symplectomorphism, also known by many authors as generating function although in fact it does not generate the symplectomorphism. We introduce variational principles not only for the orbits of a symplectomorphism, but also for the so called invariant Lagrangian graphs. We introduce the non-degenerate ones and study the minimizing ones. Applications are also given for a broad class of examples.

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