The local period function for Hamiltonian systems with applications
In the first part of the paper we develop a constructive procedure to obtain the Taylor expansion, in terms of the energy, of the period function for a non-degenerated center of any planar analytic Hamiltonian system. We apply it to several examples, including the whirling pendulum and a cubic Hamil...
| Autores: | , , |
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| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2021 |
| País: | Brasil |
| Recursos: | Universidade Estadual Paulista (UNESP) |
| Repositório: | Repositório Institucional da UNESP |
| Idioma: | inglês |
| OAI Identifier: | oai:repositorio.unesp.br:11449/210058 |
| Acesso em linha: | http://dx.doi.org/10.1016/j.jde.2021.01.033 http://hdl.handle.net/11449/210058 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Period function Limit cycles Abelian integrals Extended complete Chebyshev systems Picard-Fuchs differential equations |
| Resumo: | In the first part of the paper we develop a constructive procedure to obtain the Taylor expansion, in terms of the energy, of the period function for a non-degenerated center of any planar analytic Hamiltonian system. We apply it to several examples, including the whirling pendulum and a cubic Hamiltonian system. The knowledge of this Taylor expansion of the period function for this system is one of the key points to study the number of zeroes of an Abelian integral that controls the number of limit cycles bifurcating from the periodic orbits of a planar Hamiltonian system that is inspired by a physical model on capillarity. Several other classical tools, like for instance Chebyshev systems are applied to study this number of zeroes. The approach introduced can also be applied in other situations. (C) 2021 Elsevier Inc. All rights reserved. |
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