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Connecting Symmetric And Asymmetric Families Of Periodic Orbits In Squared Symmetric Hamiltonians

Author

Listed:
  • FERNANDO BLESA

    (Departamento de Física Aplicada, Universidad de Zaragoza, E-50009 Zaragoza, Spain)

  • SŁAWOMIR PIASECKI

    (Departamento de Matemática Aplicada, Universidad de Zaragoza, E-50009 Zaragoza, Spain)

  • ÁNGELES DENA

    (Centro Universitario de la Defensa, Academia General Militar, E-50090 Zaragoza, Spain)

  • ROBERTO BARRIO

    (Departamento de Matemática Aplicada and IUMA, Universidad de Zaragoza, E-50009 Zaragoza, Spain)

Abstract

In this work, we study a generic squared symmetric Hamiltonian of two degrees of freedom. Our aim is to show a global methodology to analyze the evolution of the families of periodic orbits and their bifurcations. To achieve it, we use several numerical techniques such as a systematic grid search algorithm in sequential and parallel, a fast chaos indicator and a tool for the continuation of periodic orbits. Using them, we are able to study the special and generic bifurcations of multiplicity one that allow us to understand the dynamics of the system and we show in detail the evolution of some symmetric breaking periodic orbits.

Suggested Citation

  • Fernando Blesa & Sławomir Piasecki & Ángeles Dena & Roberto Barrio, 2012. "Connecting Symmetric And Asymmetric Families Of Periodic Orbits In Squared Symmetric Hamiltonians," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 23(02), pages 1-22.
    • Handle: RePEc:wsi:ijmpcx:v:23:y:2012:i:02:n:s0129183112500143
    DOI: 10.1142/S0129183112500143
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