The criticality of centers of potential systems at the outer boundary
The number of critical periodic orbits that bifurcate from the outer boundary of a potential center is studied. We call this number the criticality at the outer boundary. Our main results provide sufficient conditions in order to ensure that this number is exactly 0 and 1. We apply them to study the...
| Autores: | , , |
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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:169462 |
| Acceso en línea: | https://ddd.uab.cat/record/169462 https://dx.doi.org/urn:doi:10.1016/j.jde.2015.11.040 |
| Access Level: | acceso abierto |
| Palabra clave: | Bifurcation Center Critical periodic orbit Criticality Period function |
| Sumario: | The number of critical periodic orbits that bifurcate from the outer boundary of a potential center is studied. We call this number the criticality at the outer boundary. Our main results provide sufficient conditions in order to ensure that this number is exactly 0 and 1. We apply them to study the bifurcation diagram of the period function of X = -y∂ x ((x 1) p - (x 1) q )∂ y with q < p. This family was previously studied for q = 1 by Y. Miyamoto and K. Yagasaki. |
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