Heteroclinic bifurcations near Hopf-zero bifurcation in reversible vector fields in R-3

dc.creatorLamb, JSW
dc.creatorTeixeira, MA
dc.creatorWebster, KN
dc.date2005
dc.dateDEC 1
dc.date2014-11-19T00:20:51Z
dc.date2015-11-26T17:55:07Z
dc.date2014-11-19T00:20:51Z
dc.date2015-11-26T17:55:07Z
dc.date.accessioned2018-03-29T00:38:53Z
dc.date.available2018-03-29T00:38:53Z
dc.identifierJournal Of Differential Equations. Academic Press Inc Elsevier Science, v. 219, n. 1, n. 78, n. 115, 2005.
dc.identifier0022-0396
dc.identifierWOS:000233442500004
dc.identifier10.1016/j.jde.2005.02.019
dc.identifierhttp://www.repositorio.unicamp.br/jspui/handle/REPOSIP/68280
dc.identifierhttp://www.repositorio.unicamp.br/handle/REPOSIP/68280
dc.identifierhttp://repositorio.unicamp.br/jspui/handle/REPOSIP/68280
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/1290951
dc.descriptionWe study the dynamics near a symmetric Hopf-zero (also known as saddle-node Hopf or fold-Hopf) bifurcation in a reversible vector field in R-3, with involutory an reversing symmetry whose fixed point subspace is one-dimensional. We focus on the case in which the normal form for this bifurcation displays a degenerate family of heteroclinics between two asymmetric saddle-foci. We study local perturbations of this degenerate family of heteroclinics within the class of reversible vector fields and establish the generic existence of hyperbolic basic sets (horseshoes), independent of the eigenvalues of the saddle-foci, as well as cascades of bifurcations of periodic, heteroclinic and homoclinic orbits. Finally, we discuss the application of our results to the Michelson system, describing stationary states and travelling waves of the Kuramoto-Sivashinsky PDE. (c) 2005 Elsevier Inc. All rights reserved.
dc.description219
dc.description1
dc.description78
dc.description115
dc.languageen
dc.publisherAcademic Press Inc Elsevier Science
dc.publisherSan Diego
dc.publisherEUA
dc.relationJournal Of Differential Equations
dc.relationJ. Differ. Equ.
dc.rightsfechado
dc.rightshttp://www.elsevier.com/about/open-access/open-access-policies/article-posting-policy
dc.sourceWeb of Science
dc.subjectKuramoto-sivashinsky Equation
dc.subjectTraveling-wave Solutions
dc.subjectNormal Forms
dc.subjectNilpotent Singularity
dc.subjectSteady Solutions
dc.subjectLinear-systems
dc.subjectCodimension-3
dc.subjectUnfoldings
dc.subjectOrbits
dc.titleHeteroclinic bifurcations near Hopf-zero bifurcation in reversible vector fields in R-3
dc.typeArtículos de revistas


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