Periodic orbits of a perturbed 3-dimensional isotropic oscillator with axial symmetry
Guirao, Juan Luis Garcia (Universidad Politécnica de Cartagena. Departamento de Matemática Aplicada y Estadística)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Vera, Juan A. (Universidad Politécnica de Cartagena. Centro Universitario de la Defensa)

Date:	2015
Abstract:	We study the periodic orbits of a generalized Yang-Mills Hamiltonian H depending on a parameter β. Playing with the parameter β we are considering extensions of the Contopoulos and of the Yang-Mills Hamiltonians in a 3-dimensional space. This Hamiltonian consists of a 3-dimensional isotropic harmonic oscillator plus a homogeneous potential of fourth degree having an axial symmetry, which implies that the third component N of the angular momentum is constant. We prove that in each invariant space H = h > 0 the Hamiltonian system has at least four periodic solutions if either β < 0, or β = 5 sqrt(13); and at least 12 periodic solutions if β > 6 and β != 5 sqrt(13). We also study the linear stability or instability of these periodic solutions.
Grants:	Ministerio de Economía y Competitividad MTM2011-22587 Ministerio de Economía y Competitividad MTM2008-03437 Ministerio de Economía y Competitividad MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 318999 European Commission 316338 Ministerio de Economía y Competitividad UNAB-10-4E-378
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Periodic orbits ; Averaging Theory ; 3D isotropic oscillators ; 3D Yang-Mills Hamiltonian ; Stability of periodic orbits
Published in:	Nonlinear Dynamics, Vol. 83 (2015) , p. 839-848, ISSN 1573-269X

DOI: 10.1007/s11071-015-2371-z

Postprint 15 p, 795.4 KB

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