MPEJ Volume 10, No. 5, 45 pp.
Received: Mar 2, 2004. Accepted: Mar 23, 2004.

R. de la Llave, C.E. Wayne
Whiskered and low dimensional tori in nearly integrable
Hamiltonian systems

ABSTRACT: We show that a nearly integrable hamiltonian system has
invariant tori of all dimensions smaller than the number of degrees of
freedom provided that certain nondegeneracy conditions are met. The
tori we construct are generated by the resonances of the system and
are topologically different from the orbits that are present in the
integrable system. We also show that the tori we construct have stable
and unstable manifolds and point out how to construct other types of
interesting orbits.

The method of proof is a combination of different perturbation methods.


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http://www.ma.utexas.edu/mpej/Vol/10/5.ps
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http://mpej.unige.ch/mpej/Vol/10/5.ps
http://mpej.unige.ch/mpej/Vol/10/5.pdf