Please use this identifier to cite or link to this item: http://hdl.handle.net/2445/33826
Title: On the computation of reducible invariant tori on a parallel computer
Author: Jorba i Monte, Àngel
Olmedo, Estrella
Keywords: Dinàmica
Teoria ergòdica
Algorismes
Dynamics
Ergodic theory
Algorithms
Issue Date: 2009
Publisher: Society for Industrial and Applied Mathematics.
Abstract: We present an algorithm for the computation of reducible invariant tori of discrete dynamical systems that is suitable for tori of dimensions larger than 1. It 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 (flows) to show the efficiency of the method in a parallel computer. In these flows we compute invariant tori of dimensions up to 5, by taking suitable sections.
Note: Reproducció del document publicat a: http://dx.doi.org/10.1137/080724563
It is part of: SIAM Journal On Applied Dynamical Systems, 2009, vol. 8, num. 4, p. 1382-1404
Related resource: http://dx.doi.org/10.1137/080724563
URI: http://hdl.handle.net/2445/33826
ISSN: 1536-0040
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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