Poincaré-Pontryagin-Melnikov functions for a class of perturbed planar Hamiltonian equations
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...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2016 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:169447 |
| Acceso en línea: | https://ddd.uab.cat/record/169447 https://dx.doi.org/urn:doi:10.1007/s12346-015-0185-5 |
| Access Level: | acceso abierto |
| Palabra clave: | Limit cycle Abelian integral Perturbed equation Hamiltonian equation |
| Sumario: | 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. |
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