TITLE:
A parameterization method for the computation of
invariant tori and their whiskers in quasi periodic maps: 
rigorous results.


AUTHORS:
Alex Haro (1) and Rafael de la Llave (2)

(1) Departament de Matematica Aplicada i Analisi,
    Universitat de Barcelona,
    Gran Via 585, 08007 Barcelona (Spain) 
    E-mail: haro@mat.ub.es
(2) Department of Mathematics,
    University of Texas at Austin,
    Austin, TX 78712 (USA).
    E-mails: llave@math.utexas.edu

ABSTRACT: 
We prove rigorous results on existence and persistence of invariant tori and 
their invariant manifolds for quasiperiodically perturbed systems. The proofs 
are based on the parametrization method of X. Cabre, E. Fontich, R. de la 
Llave, Ind. Math. Jour. 52, 2. The invariant manifolds results proved here 
include as particular cases of the usual (strong) stable and (strong) unstable 
manifolds, but also include other non-resonant manifolds. 

The method lends itself to numerical implementations whose analysis and 
implementation is studied in several companion papers by the same authors.