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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)

Data: 2013
Resum: 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.
Drets: Tots els drets reservats.
Llengua: Anglès
Document: article ; recerca ; preprint
Matèria: Polynomial differential equation ; Bifurcation of limit cycles ; Shape ; Number ; Location and period of limit cycles
Publicat a: 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/

26 p, 622.2 KB

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