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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.
Note: Número d'acord de subvenció MICIIN/MTM2011-22751
Note: Número d'acord de subvenció MICIIN/MTM2008-03437
Note: Número d'acord de subvenció AGAUR/2014/SGR-410
Rights: Tots els drets reservats.
Language: Anglès.
Document: article ; recerca ; submittedVersion
Subject: Polynomial differential equation ; Bifurcation of limit cycles ; Shape ; Number ; Location and period of limit cycles
Published in: Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods, Vol. 81 (2013) , p. 130-148, ISSN 0362-546X

DOI: 10.1016/j.na.2012.10.017


Preprint
26 p, 622.2 KB

The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (scientific output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles

 Record created 2016-05-06, last modified 2019-07-31



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