Periodic motion in perturbed elliptic oscillators revisited
Corbera Subirana, Montserrat (Universitat de Vic. Departament de Tecnologies Digitals i de la Informació)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Departamento de Matemática)

Date:	2016
Abstract:	We analytically study the Hamiltonian system in R^4 with Hamiltonian H= 12 (p_x^2 p_y^2) 12 (_1^2 x^2 _2^2 y^2)- V_1(x,y) being (a) V_1(x,y)=-(xy^2 ax^3) and (b) V_1(x,y)=-(x^2y ax^3) with aR, where is a small parameter and _1 and _2 are the unperturbed frequencies of the oscillations along the x and y axis, respectively. For the potential (a) using averaging theory of first order we analytically find for each aR eight families of periodic solutions in every positive energy level of H when the frequencies are not equal. For the potential (b) using averaging theory of first and second order we analytically find seven families of periodic solutions in every positive energy level of H when the frequencies are not equal. Four of these seven families are defined for all aR whereas the other three are defined for all a 0. Moreover, we provide the shape of all these families of periodic solutions. These Hamiltonians may represent the central parts of deformed galaxies and thus have been extensively used and studied numerically in order to describe local motion in galaxies near an equilibrium point.
Grants:	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
Note:	Agraïments: The third author is partially supported by FCT/Portugal through UID/MAT/04459/2013.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Averaging theory ; Galactic potential
Published in:	Astrophysics and Space Science. An International Journal of Astronomy, Astrophysics and Space Science, Vol. 361:348 (2016) , p. 1-8, ISSN 1572-946X

DOI: 10.1007/s10509-016-2927-5

Postprint 23 p, 689.0 KB

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