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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 716024, 12 pages
http://dx.doi.org/10.1155/2012/716024
Research Article

High-Precision Continuation of Periodic Orbits

1Centro Universitario de la Defensa and IUMA, 50090 Zaragoza, Spain
2Departamento de Matemática Aplicada and IUMA, Universidad de Zaragoza, 50009 Zaragoza, Spain

Received 30 December 2011; Accepted 14 February 2012

Academic Editor: Muhammad Aslam Noor

Copyright © 2012 Ángeles Dena et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Obtaining periodic orbits of dynamical systems is the main source of information about how the orbits, in general, are organized. In this paper, we extend classical continuation algorithms in order to be able to obtain families of periodic orbits with high-precision. These periodic orbits can be corrected to get them with arbitrary precision. We illustrate the method with two important classical Hamiltonian problems.