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dc.contributor.authorBonet Revés, Carles
dc.contributor.authorFernandes Larrosa, Juliana
dc.contributor.authorMartínez-Seara Alonso, M. Teresa
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.date.accessioned2018-09-18T11:43:40Z
dc.date.issued2018-09-05
dc.identifier.citationBonet, C., Fernandes, J., Martinez-seara, T. Regularization around a generic codimension one fold-fold singularity. "Journal of differential equations", 5 Setembre 2018, vol. 265, núm. 5, p. 1761-1838.
dc.identifier.issn0022-0396
dc.identifier.otherhttps://arxiv.org/abs/1605.02376
dc.identifier.urihttp://hdl.handle.net/2117/121257
dc.description.abstractThis paper is devoted to study the generic fold-fold singularity of Filippov systems on the plane, its unfoldings and its Sotomayor–Teixeira regularization. We work with general Filippov systems and provide the bifurcation diagrams of the fold-fold singularity and their unfoldings, proving that, under some generic conditions, is a codimension one embedded submanifold of the set of all Filippov systems. The regularization of this singularity is studied and its bifurcation diagram is shown. In the visible–invisible case, the use of geometric singular perturbation theory has been useful to give the complete diagram of the unfolding, specially the appearance and disappearance of periodic orbits that are not present in the Filippov vector field. In the case of a linear regularization, we prove that the regularized system is equivalent to a general slow-fast system studied by Krupa and Szmolyan
dc.format.extent78 p.
dc.language.isoeng
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject.lcshPerturbation (Mathematics)
dc.subject.otherNon-smooth systems
dc.subject.otherRegularization
dc.subject.otherBifurcations Melnikov method
dc.subject.otherSingular perturbation theory.
dc.titleRegularization around a generic codimension one fold-fold singularity
dc.typeArticle
dc.subject.lemacPertorbació (Matemàtica)
dc.subject.lemacSistemes dinàmics diferenciables
dc.contributor.groupUniversitat Politècnica de Catalunya. SD - Sistemes Dinàmics de la UPC
dc.identifier.doi10.1016/j.jde.2018.04.047
dc.description.peerreviewedPeer Reviewed
dc.relation.publisherversionhttps://www.sciencedirect.com/science/article/pii/S0022039618302468
dc.rights.accessRestricted access - publisher's policy
drac.iddocument23170464
dc.description.versionPostprint (published version)
dc.date.lift2020-09-05
upcommons.citation.authorBonet, C., Fernandes, J., Martinez-seara, Tere
upcommons.citation.publishedtrue
upcommons.citation.publicationNameJournal of differential equations
upcommons.citation.volume265
upcommons.citation.number5
upcommons.citation.startingPage1761
upcommons.citation.endingPage1838


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Except where otherwise noted, content on this work is licensed under a Creative Commons license: Attribution-NonCommercial-NoDerivs 3.0 Spain