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...
| Authors: | ; |
|---|---|
| Format: | Article |
| Status: | Accepted version |
| Publication date: | 2017 |
| Country: | España |
| Institution: | Universitat de Lleida (UdL) |
| Repository: | Repositori Obert UdL |
| OAI Identifier: | oai:repositori.udl.cat:10459.1/62956 |
| Online Access: | https://doi.org/10.1016/j.aml.2017.03.004 http://hdl.handle.net/10459.1/62956 |
| Access Level: | Open access |
| Keyword: | Center problem Analytic integrability Strong saddle |
| _version_ | 1878737124975443968 |
|---|---|
| author | Giné, Jaume |
| author2 | Llibre, Jaume |
| author2_role | author |
| author_browse | Giné, Jaume Llibre, Jaume |
| author_facet | Giné, Jaume Llibre, Jaume |
| author_role | author |
| collection | Repositori Obert UdL |
| 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. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ES_9b0fafa0c19f9bba3bc06c5a8815a3ac |
| institution | Universitat de Lleida (UdL) |
| instname_str | Universitat de Lleida (UdL) |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:repositori.udl.cat:10459.1/62956 |
| publishDate | 2017 |
| publishDateSort | 2017 |
| publisher | Elsevier |
| publisherStr | Elsevier |
| reponame_str | Repositori Obert UdL |
| spelling | 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 |
| spellingShingle | On the Integrability of Liénard systems with a strong saddle Giné, Jaume Center problem Analytic integrability Strong saddle |
| status_str | acceptedVersion |
| title | 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_short | On the Integrability of Liénard systems with a strong saddle |
| title_sort | On the Integrability of Liénard systems with a strong saddle |
| topic | Center problem Analytic integrability Strong saddle |
| topic_facet | Center problem Analytic integrability Strong saddle |
| url | https://doi.org/10.1016/j.aml.2017.03.004 http://hdl.handle.net/10459.1/62956 |