R. de la Llave, C. E. Wayne 
Whiskered and low dimensional tori in nearly integrable Hamiltonian systems
(512K, pdf)

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.