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:...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | Universitat de Lleida (UdL) |
| Repositorio: | Repositori Obert UdL |
| OAI Identifier: | oai:repositori.udl.cat:10459.1/62956 |
| Acceso en línea: | https://doi.org/10.1016/j.aml.2017.03.004 http://hdl.handle.net/10459.1/62956 |
| Access Level: | acceso abierto |
| Palabra clave: | Center problem Analytic integrability Strong saddle |
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oai:repositori.udl.cat:10459.1/62956 |
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ES |
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España |
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On the Integrability of Liénard systems with a strong saddle Giné, Jaume Llibre, Jaume Center problem Analytic integrability 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 $[p:-q]$ 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. The first author is partially supported by a MINECO/FEDER grant number MTM2014- 53703-P and an AGAUR (Generalitat de Catalunya) grant number 2014SGR-1204. The second author is partially supported by a FEDER-MINECO grant MTM2016-77278-P, a MINEC0 grant MTM2013-40998-P, and an AGAUR grant number 2014SGR-568. Elsevier https://doi.org/10.1016/j.aml.2017.03.004 http://hdl.handle.net/10459.1/62956 |
| title |
On the Integrability of Liénard systems with a strong saddle |
| spellingShingle |
On the Integrability of Liénard systems with a strong saddle Giné, Jaume Center problem Analytic integrability Strong saddle |
| title_short |
On the Integrability of Liénard systems with a strong saddle |
| title_full |
On the Integrability of Liénard systems with a strong saddle |
| title_fullStr |
On the Integrability of Liénard systems with a strong saddle |
| title_full_unstemmed |
On the Integrability of Liénard systems with a strong saddle |
| title_sort |
On the Integrability of Liénard systems with a strong saddle |
| author |
Giné, Jaume |
| author_facet |
Giné, Jaume Llibre, Jaume |
| author_role |
author |
| author2 |
Llibre, Jaume |
| author2_role |
author |
| topic |
Center problem Analytic integrability Strong saddle |
| topic_facet |
Center problem Analytic integrability Strong saddle |
| description |
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. |
| publishDate |
2017 |
| format |
article |
| status_str |
acceptedVersion |
| url |
https://doi.org/10.1016/j.aml.2017.03.004 http://hdl.handle.net/10459.1/62956 |
| eu_rights_str_mv |
openAccess |
| publisher |
Elsevier |
| institution |
Universitat de Lleida (UdL) |
| collection |
Repositori Obert UdL |
| reponame_str |
Repositori Obert UdL |
| instname_str |
Universitat de Lleida (UdL) |
| _version_ |
1878737124975443968 |
| publishDateSort |
2017 |
| author_browse |
Giné, Jaume Llibre, Jaume |
| publisherStr |
Elsevier |
| score |
6,8972664 |