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The European Physical Journal Special Topics

, Volume 223, Issue 13, pp 2705–2722 | Cite as

Continuation of periodic orbits in symmetric Hamiltonian and conservative systems

  • J. Galan-Vioque
  • F. J. M. Almaraz
  • E. F. Macías
Review
Part of the following topical collections:
  1. Advanced Computational and Experimental Techniques in Nolinear Dynamics. Guest Editors: Elbert E.N. Macau and Carlos L. Pando Lambruschini (Eds.)

Abstract

We present and review results on the continuation and bifurcation of periodic solutions in conservative, reversible and Hamiltonian systems in the presence of symmetries. In particular we show how two-point boundary value problem continuation software can be used to compute families of periodic solutions of symmetric Hamiltonian systems. The technique is introduced with a very simple model example (the mathematical pendulum), justified with a theoretical continuation result and then applied to two non trivial examples: the non integrable spring pendulum and the continuation of the figure eight solution of the three body problem.

Keywords

Periodic Solution Periodic Orbit Hamiltonian System European Physical Journal Special Topic Bifurcation Diagram 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© EDP Sciences and Springer 2014

Authors and Affiliations

  • J. Galan-Vioque
    • 1
  • F. J. M. Almaraz
    • 2
  • E. F. Macías
    • 1
  1. 1.Departamento de Matemática Aplicada II e Instituto de Matemáticas de la Universidad de SevillaSevillaSpain
  2. 2.Departamento de Ciencias Físicas, Matemáticas y de la ComputaciónUniversidad Cardenal HerreraAlfara del Patriarca - ValenciaSpain

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