Periodic orbits near equilibria via averaging theory of second order
Lyapunov, Weinstein and Moser obtained remarkable theorems giving sufficient conditions for the existence of periodic orbits emanating from an equilibrium point of a differential system with a first integral. Using averaging theory of first order we established in [1] a similar result for a differen...
| Autores: | , , |
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| Formato: | artículo |
| Fecha de publicación: | 2012 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:150561 |
| Acesso em linha: | https://ddd.uab.cat/record/150561 https://dx.doi.org/urn:doi:10.3846/13926292.2012.736090 |
| Access Level: | acceso abierto |
| Palavra-chave: | Periodic orbit Averaging theory of second order Hopf bifurcation |
| Resumo: | Lyapunov, Weinstein and Moser obtained remarkable theorems giving sufficient conditions for the existence of periodic orbits emanating from an equilibrium point of a differential system with a first integral. Using averaging theory of first order we established in [1] a similar result for a differential system without assuming the existence of a first integral. Now, using averaging theory of second order, we extend our result to the case when the first order average is identically zero. Our result can be interpreted as a kind of special Hopf bifurcation. |
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