Poincaré–Pontryagin–Melnikov Functions for a Type of Perturbed Degenerate Hamiltonian Equations
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Salomón Rebollo-Perdomo [1]
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[1] Universidad del Bío-Bío
Universidad del Bío-Bío
Comuna de Concepción, Chile
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- Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 16, Nº 1, 2017, págs. 149-174
- Idioma: inglés
- Texto completo no disponible (Saber más ...)
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Resumen
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.
