Below is the ascii version of the abstract for 14-61. The html version should be ready soon.

Massimiliano Berti, Philippe Bolle
A Nash-Moser approach to KAM theory
(398K, PDF)

ABSTRACT.  Any finite dimensional embedded invariant torus of an Hamiltonian system, 
densely filled by quasi-periodic solutions, is isotropic. This property allows us 
to construct a set of symplectic coordinates in a neighborhood of the torus in which 
the Hamiltonian is in a generalized KAM normal form with angle-dependent coefficients. 
Based on this observation we develop an approach to KAM theory via 
a Nash-Moser implicit function iterative theorem. The key point is to construct an 
approximate right inverse of the differential operator associated to the linearized 
Hamiltonian system at each approximate quasi-periodic solution. In the above symplectic 
coordinates the linearized dynamics on the tangential and normal directions 
to the approximate torus are approximately decoupled. The construction of an approximate 
inverse is thus reduced to solving a quasi-periodically forced linear differential 
equation in the normal variables. Applications of this procedure allow to 
prove the existence of finite dimensional Diophantine invariant tori of autonomous 
PDE's