Home > Articles > Published articles > Poincaré-Pontryagin-Melnikov functions for a class of perturbed planar Hamiltonian equations |
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 |
Postprint 24 p, 485.3 KB |