TITLE:
On the computation of reducible invariant tori in a parallel computer

AUTHORS:
Angel Jorba and Estrella Olmedo
Departament de Matematica Aplicada i Analisi.
Universitat de Barcelona.
Gran Via 585, 08007, Barcelona, Spain.
E-mails: angel@maia.ub.es, estrella@maia.ub.es

ABSTRACT:
We present an algorithm for the computation of reducible
quasi-periodic solutions of discrete dynamical systems. The method is
based on a quadratically convergent scheme that approximates, at the
same time, the Fourier series of the torus, its Floquet transformation
and its Floquet matrix. The Floquet matrix describes the linearization
of the dynamics around the torus and, hence, its linear stability.

The algorithm presents a high degree of parallelism and the
computational effort grows linearly with the number of Fourier modes
needed to represent the solution. For these reasons it is a very good
option to compute quasi-periodic solutions with several basic
frequencies. The paper includes some examples to show the efficiency
of the method in a parallel computer.