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dc.contributor.authorGarcía, I. A. (Isaac A.)
dc.contributor.authorHernández Bermejo, Benito
dc.date.accessioned2017-08-31T07:48:20Z
dc.date.available2018-07-14T22:21:00Z
dc.date.issued2017-07-15
dc.identifier.issn1751-8113
dc.identifier.urihttp://hdl.handle.net/10459.1/60207
dc.description.abstractSome aspects of the relationship between conservativeness of a dynamical system (namely the preservation of a finite measure) and the existence of a Poisson structure for that system are analyzed. From the local point of view, due to the Flow-Box Theorem we restrict ourselves to neighborhoods of singularities. In this sense, we characterize Poisson structures around the typical zero-Hopf singularity in dimension 3 under the assumption of having a local analytic first integral with non-vanishing first jet by connecting with the classical Poincar\'e center problem. From the global point of view, we connect the property of being strictly conservative (the invariant measure must be positive) with the existence of a Poisson structure depending on the phase space dimension. Finally, weak conservativeness in dimension two is introduced by the extension of inverse Jacobi multipliers as weak solutions of its defining partial differential equation and some of its applications are developed. Examples including Lotka-Volterra systems, quadratic isochronous centers, and non-smooth oscillators are provided.
dc.description.sponsorshipBoth authors would like to acknowledge Ministerio de Econom´ıa y Competitividad for Project Ref. MTM2014-53703-P. In addition, I.A.G. acknowledges AGAUR grant number 2014SGR 1204. B.H.-B. acknowledges Ministerio de Econom´ıa y Competitividad for Project Ref. MTM2016-80276-P as well as financial support from Universidad Rey Juan Carlos-Banco de Santander (Excellence Group QUINANOAP, grant number 30VCPIGI14). Finally, B.H.-B. is sincerely indebted to the members of Departament de Matemàtica, Universitat de Lleida, for their kind hospitality
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherIOP Publishing
dc.relationMINECO/PN2013-2016/MTM2014-53703-P
dc.relationMINECO/PN2013-2016/MTM2016-80276-P
dc.relation.isformatofVersió postprint del document publicat a https://doi.org/10.1088/1751-8121/aa7bda
dc.relation.ispartofJournal of Physics A: Mathematical and Theoretical, 2017, vol. 50, p. 1-17
dc.rights(c) IOP Publishing, 2017
dc.subjectMatemáticas
dc.subjectInverse Jacobi multipliers
dc.subjectConservative systems
dc.subjectPoisson systems
dc.titleInverse Jacobi multiplier as a link between conservative systems and Poisson structures
dc.typeinfo:eu-repo/semantics/article
dc.date.updated2017-08-31T07:48:21Z
dc.identifier.idgrec025812
dc.type.versioninfo:eu-repo/semantics/acceptedVersion
dc.rights.accessRightsinfo:eu-repo/semantics/openAccess
dc.identifier.doihttps://doi.org/10.1088/1751-8121/aa7bda


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