dc.contributor.author Giné, Jaume dc.contributor.author Llibre, Jaume dc.date.accessioned 2018-04-03T11:38:20Z dc.date.available 2019-08-01T22:15:35Z dc.date.issued 2017 dc.identifier.issn 0893-9659 dc.identifier.uri http://hdl.handle.net/10459.1/62956 dc.description.abstract 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. dc.description.sponsorship 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. dc.format.mimetype application/pdf dc.language.iso eng dc.publisher Elsevier dc.relation MINECO/PN2013-2016/MTM2014-53703-P dc.relation MINECO/PN2013-2016/MTM2013-40998-P dc.relation MINECO/PN2013-2016/MTM2016-77278-P dc.relation.isformatof Versió postprint del document publicat a http://dx.doi.org/10.1016/j.aml.2017.03.004 dc.relation.ispartof Applied Mathematics Letters, 2017, vol. 70, p. 39-45 dc.rights cc-by-nc-nd (c) Elsevier, 2017 dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es dc.subject Center problem dc.subject Analytic integrability dc.subject Strong saddle dc.title On the Integrability of Liénard systems with a strong saddle dc.type info:eu-repo/semantics/article dc.date.updated 2018-04-03T11:38:20Z dc.identifier.idgrec 025843 dc.type.version info:eu-repo/semantics/acceptedVersion dc.rights.accessRights info:eu-repo/semantics/openAccess dc.identifier.doi https://doi.org/10.1016/j.aml.2017.03.004
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