Shape and period of limit cycles bifurcating from a class of Hamiltonian period annulus
Prohens, Rafel (Universitat de les Illes Balears. Departament de Ciències Matemàtiques i Informàtica)
Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2013
Abstract:	In this work we are concerned with the problem of shape and period of isolated periodic solutions of perturbed analytic radial Hamiltonian vector fields in the plane. Fran¸coise develop a method to obtain the first non vanishing Poincaré-Pontryagin-Melnikov function. We generalize this technique and we apply it to know, up to any order, the shape of the limit cycles bifurcating from the period annulus of the class of radial Hamiltonians. We write any solution, in polar coordinates, as a power series expansion in terms of the small parameter. This expansion is also used to give the period of the bifurcated periodic solutions. We present the concrete expression of the solutions up to third order of perturbation of Hamiltonians of the form H = H(r). Necessary and sufficient conditions that show if a solution is simple or double are also presented.
Grants:	Ministerio de Ciencia e Innovación MTM2011-22751 Ministerio de Ciencia e Innovación MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-410
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Polynomial differential equation ; Bifurcation of limit cycles ; Shape ; Number ; Location and period of limit cycles
Published in:	Nonlinear Analysis : Theory, Methods and Applications, Vol. 81 (2013) , p. 130-148, ISSN 0362-546X

DOI: 10.1016/j.na.2012.10.017

Postprint 26 p, 622.2 KB

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