On the Integrability of Liénard systems with a strong saddle
We study the local analytic integrability for real Li\'{e}nard systems, $\dot x=y-F(x),$ $\dot y= x$, with $F(0)=0$ but $F'(0)\ne0,$ which implies that it has a strong saddle at the origin. First we prove that this problem is equivalent to study the local analytic integrability of the $[p:-q]$ reson...
| Autores: | ; |
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| Tipo de documento: | Artigo |
| Estado: | Accepted version |
| Data de publicação: | 2017 |
| País: | España |
| Recursos: | Universitat de Lleida (UdL) |
| Repositório: | Repositori Obert UdL |
| OAI Identifier: | oai:repositori.udl.cat:10459.1/62956 |
| Acesso em linha: | https://doi.org/10.1016/j.aml.2017.03.004 http://hdl.handle.net/10459.1/62956 |
| Nível de acesso: | Acesso aberto |
| Palavra-chave: | Center problem Analytic integrability Strong saddle |
| Resumo: | We study the local analytic integrability for real Li\'{e}nard systems, $\dot x=y-F(x),$ $\dot y= x$, with $F(0)=0$ but $F'(0)\ne0,$ which implies that it has a strong saddle at the origin. First we prove that this problem is equivalent to study the local analytic integrability of the $[p:-q]$ resonant saddles. This result implies that the local analytic integrability of a strong saddle is a hard problem and only partial results can be obtained. Nevertheless this equivalence gives a new method to compute the so-called resonant saddle quantities transforming the $[p:-q]$ resonant saddle into a strong saddle. |
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