TITLE:
KAM theory without action-angle variables

AUTHORS:
Rafael de la Llave^(1), Alejandra Gonzalez^(1) Angel Jorba^(2),
Jordi Villanueva^(3).

(1) llave@math.utexas.edu, alego@math.utexas.edu
Department of Mathematics 
University of Texas at Austin 
Austin, TX 78712, USA

(2) angel@maia.ub.es
Departament de Matematica Aplicada i Analisi,
Universitat de Barcelona,
Gran Via 585, 08007 Barcelona, Spain.

(3) jordi@vilma.upc.es
Departament de Matematica Aplicada I,
Universitat Politecnica de Catalunya,
Diagonal 647, 08028 Barcelona, Spain.

ABSTRACT:
Given a torus approximately invariant under a symplectic map, we find
sufficient conditions for the existence of a true invariant torus
close to the given one.  We do not assume either that we are working
on action-angle variables nor that the map is close to integrable.
The proposed method is also useful to compute numerically invariant
tori for symplectic maps. Analogous results are also true for vector
fields.