Period Function for a Family of Piecewise Planar Hamiltonian Systems
In this paper, we analyze the monotonicity and the number of critical periods of the period function associated with a family of piecewise planar continuous potential systems. In particular, we describe the bifurcation diagram of the period function, determining the regions of the parameter space wh...
| Autores: | , , |
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| Formato: | artículo |
| Fecha de publicación: | 2024 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:307727 |
| Acesso em linha: | https://ddd.uab.cat/record/307727 https://dx.doi.org/urn:doi:10.1142/S0218127424501992 |
| Access Level: | acceso abierto |
| Palavra-chave: | Piecewise planar Hamiltonian system Period function Monotonicity Critical period Bifurcation diagram |
| Resumo: | In this paper, we analyze the monotonicity and the number of critical periods of the period function associated with a family of piecewise planar continuous potential systems. In particular, we describe the bifurcation diagram of the period function, determining the regions of the parameter space where it is monotonically increasing or decreasing and where it has at most one simple critical period. In order to prove the main result, we rewrite such a function in terms of the two period functions of the uncoupled planar Hamiltonian systems matched by the separation line. |
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