Poincaré-Pontryagin-Melnikov functions for a class of perturbed planar Hamiltonian equations
Rebollo-Perdomo, Salomón (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2016
Abstract:	In this paper we consider polynomial perturbations of a family of polynomial Hamiltonian equations whose associated Hamiltonian is not transversal to infinity, and its complexification is not a Morse polynomial. We look for an algorithm to compute the first non-vanishing Poincaré-Pontryagin-Melnikov function of the displacement function associated with the perturbed equation. We show that the algorithm of the case when the Hamiltonian is transversal to infinity and its complexification is a Morse polynomial can be extended to our family of perturbed equations. We apply the result to study the maximum number of zeros of the first non-vanishing Poincaré-Pontryagin-Melnikov function associated with some perturbed Hamiltonian equations.
Note:	Agraïments: The author would like to thank the Centre de Recerca Matemàtica for their support and hospitality during the period in which the main results of this paper were obtained.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Limit cycle ; Abelian integral ; Perturbed equation ; Hamiltonian equation
Published in:	Qualitative theory of dynamical systems, 2016 , ISSN 1662-3592

DOI: 10.1007/s12346-015-0185-5

Postprint 24 p, 485.3 KB

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