CONNECTING SYMMETRIC AND ASYMMETRIC FAMILIES OF PERIODIC ORBITS IN SQUARED SYMMETRIC HAMILTONIANS

Fernando Blesa (), Sławomir Piasecki (), Ángeles Dena () and Roberto Barrio ()
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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

International Journal of Modern Physics C (IJMPC), 2012, vol. 23, issue 02, 1-22

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.

Keywords: Periodic orbits; symmetric Hamiltonians; bifurcations of periodic orbits; 05.45.-a; 05.45.Pq (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1142/S0129183112500143

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