TITLE:
KAM Theory Without Action-Angle Coordinates

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

(1) Departament de Matematica Aplicada i Analisi,
    Universitat de Barcelona,
    Gran Via 585, 08007 Barcelona (Spain) 
    E-mails: gonzalez@maia.ub.es, angel@maia.ub.es

(2) Department of Mathematics,
    University of Texas at Austin,
    Austin, TX 78712 (USA).
    E-mail: llave@math.utexas.edu

(3) Dept. de Matematica Aplicada I (ETSEIB),
    Universitat Politecnica de Catalunya,
    Diagonal 647, 08028 Barcelona (Spain).
    E-mail: jordi@tere.upc.es


ABSTRACT:
The classical KAM methods, strongly supported on the use of canonical
transformations in the action-angle context, are not efficient to be
applied to a wide range of systems in which the Hamiltonian is known
(for instance) written in Cartesian coordinates.

In this communication we present some ideas to deal with KAM theory
using ``parameterizations'' instead of ``transformations'' and
``graphs'', which we think is an efficient way to work with a more
general class of Hamiltonian systems than the classical methods (in
particular, for systems motivated by real world problems).  With the
present approach, we can extend several well-known results of KAM
theory to these systems, even when the classical statements are
difficult to be applied.
