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dc.contributor.authorGiné, Jaume
dc.contributor.authorLlibre, Jaume
dc.date.accessioned2018-04-03T11:38:20Z
dc.date.available2019-08-01T22:15:35Z
dc.date.issued2017
dc.identifier.issn0893-9659
dc.identifier.urihttp://hdl.handle.net/10459.1/62956
dc.description.abstractWe 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.sponsorshipThe 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.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherElsevier
dc.relationMINECO/PN2013-2016/MTM2014-53703-P
dc.relationMINECO/PN2013-2016/MTM2013-40998-P
dc.relationMINECO/PN2013-2016/MTM2016-77278-P
dc.relation.isformatofVersió postprint del document publicat a http://dx.doi.org/10.1016/j.aml.2017.03.004
dc.relation.ispartofApplied Mathematics Letters, 2017, vol. 70, p. 39-45
dc.rightscc-by-nc-nd (c) Elsevier, 2017
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es
dc.subjectCenter problem
dc.subjectAnalytic integrability
dc.subjectStrong saddle
dc.titleOn the Integrability of Liénard systems with a strong saddle
dc.typeinfo:eu-repo/semantics/article
dc.date.updated2018-04-03T11:38:20Z
dc.identifier.idgrec025843
dc.type.versioninfo:eu-repo/semantics/acceptedVersion
dc.rights.accessRightsinfo:eu-repo/semantics/openAccess
dc.identifier.doihttps://doi.org/10.1016/j.aml.2017.03.004


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cc-by-nc-nd (c) Elsevier, 2017
Except where otherwise noted, this item's license is described as cc-by-nc-nd (c) Elsevier, 2017