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dc.creatorCarmona Centeno, Victorianoes
dc.creatorFernández Sánchez, Fernandoes
dc.date.accessioned2021-12-02T11:52:05Z
dc.date.available2021-12-02T11:52:05Z
dc.date.issued2021-12
dc.identifier.citationCarmona Centeno, V. y Fernández Sánchez, F. (2021). Integral characterization for Poincaré half-maps in planar linear systems. Journal of Differential Equations, 305 (December), 319-346.
dc.identifier.issn0022-0396es
dc.identifier.urihttps://hdl.handle.net/11441/127947
dc.description.abstractThe intrinsic nature of a problem usually suggests a first suitable method to deal with it. Unfortunately, the apparent ease of application of these initial approaches may make their possible flaws seem to be inherent to the problem and often no alternative ways to solve it are searched for. For instance, since linear systems of differential equations are easy to integrate, Poincaré half-maps for piecewise linear systems are always studied by using the direct integration of the system in each zone of linearity. However, this approach is accompanied by two important defects: due to the different spectra of the involved matrices, many cases and strategies must be considered and, since the flight time appears as a new variable, nonlinear complicated equations arise. This manuscript is devoted to present a novel theory to characterize Poincaré half-maps in planar linear systems, that avoids the computation of their solutions and the problems it causes. This new perspective rests on the use of line integrals of a specific conservative vector field which is orthogonal to the flow of the linear system. Besides the obvious mathematical interest, this approach is attractive because it allows to simplify the study of piecewise-linear systems and deal with open problems in this field.es
dc.description.sponsorshipMinisterio de Economía y Competitividad (Spain) / FEDER MTM2014-56272-C2-1-Pes
dc.description.sponsorshipMinisterio de Economía y Competitividad (Spain) / FEDER MTM2015-65608-Pes
dc.description.sponsorshipMinisterio de Economía y Competitividad (Spain) / FEDER MTM2017-87915-C2-1-Pes
dc.description.sponsorshipMinisterio de Economía y Competitividad (Spain) / FEDER PGC2018-096265-B-I00es
dc.description.sponsorshipConsejería de Educación y Ciencia de la Junta de Andalucía (Spain) TIC-0130es
dc.description.sponsorshipConsejería de Educación y Ciencia de la Junta de Andalucía (Spain) P12-FQM-1658es
dc.description.sponsorshipConsejería de Educación y Ciencia de la Junta de Andalucía (Spain) P20_01160es
dc.formatapplication/pdfes
dc.format.extent28 p.es
dc.language.isoenges
dc.publisherElsevieres
dc.relation.ispartofJournal of Differential Equations, 305 (December), 319-346.
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internacional*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.subjectPiecewise planar linear systemses
dc.subjectPoincaré half-mapses
dc.subjectInverse integrating factorses
dc.titleIntegral characterization for Poincaré half-maps in planar linear systemses
dc.typeinfo:eu-repo/semantics/articlees
dc.type.versioninfo:eu-repo/semantics/publishedVersiones
dc.rights.accessrightsinfo:eu-repo/semantics/openAccesses
dc.contributor.affiliationUniversidad de Sevilla. Departamento de Matemática Aplicada IIes
dc.relation.projectIDMTM2014-56272-C2-1-Pes
dc.relation.projectIDMTM2015-65608-Pes
dc.relation.projectIDMTM2017-87915-C2-1-Pes
dc.relation.projectIDPGC2018-096265-B-I00es
dc.relation.projectIDTIC-0130es
dc.relation.projectIDP12-FQM-1658es
dc.relation.projectIDP20_01160es
dc.relation.publisherversionhttps://www.sciencedirect.com/science/article/pii/S0022039621006227#!es
dc.identifier.doi10.1016/j.jde.2021.10.010es
dc.contributor.groupUniversidad de Sevilla. TIC130: Investigación en Sistemas Dinámicos en Ingenieríaes
dc.journaltitleJournal of Differential Equationses
dc.publication.volumen305es
dc.publication.issueDecemberes
dc.publication.initialPage319es
dc.publication.endPage346es

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