The role of extreme orbits in the global organization of periodic regions in parameter space for one dimensional maps

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dc.contributor.authorDa Costa, Diogo Ricardo [UNESP]
dc.contributor.authorHansen, Matheus [UNESP]
dc.contributor.authorGuarise, Gustavo [UNESP]
dc.contributor.authorMedrano-T, Rene O.
dc.contributor.authorLeonel, Edson D. [UNESP]
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.contributor.institutionUniv. São Paulo
dc.contributor.institutionUniversidade Federal de São Paulo (UNIFESP)
dc.contributor.institutionImperial College London
dc.contributor.institutionAbdus Salam International Center for Theoretical Physics
dc.date.accessioned2018-12-11T16:41:28Z
dc.date.available2018-12-11T16:41:28Z
dc.date.issued2016-04-22
dc.description.abstractWe show that extreme orbits, trajectories that connect local maximum and minimum values of one dimensional maps, play a major role in the parameter space of dissipative systems dictating the organization for the windows of periodicity, hence producing sets of shrimp-like structures. Here we solve three fundamental problems regarding the distribution of these sets and give: (i) their precise localization in the parameter space, even for sets of very high periods; (ii) their local and global distributions along cascades; and (iii) the association of these cascades to complicate sets of periodicity. The extreme orbits are proved to be a powerful indicator to investigate the organization of windows of periodicity in parameter planes. As applications of the theory, we obtain some results for the circle map and perturbed logistic map. The formalism presented here can be extended to many other different nonlinear and dissipative systems.en
dc.description.affiliationDepartamento de Física UNESP-Universidade Estadual Paulista, Av. 24A, 1515, Bela Vista
dc.description.affiliationInstituto de Física Univ. São Paulo, Rua do Matão, Cidade Universitária
dc.description.affiliationDepartamento de Ciências Exatas e da Terra UNIFESP - Universidade Federal de São Paulo, Rua São Nicolau, 210
dc.description.affiliationDepartment of Mathematics Imperial College London
dc.description.affiliationAbdus Salam International Center for Theoretical Physics, Strada Costiera 11
dc.description.affiliationUnespDepartamento de Física UNESP-Universidade Estadual Paulista, Av. 24A, 1515, Bela Vista
dc.format.extent1610-1614
dc.identifierhttp://dx.doi.org/10.1016/j.physleta.2016.02.049
dc.identifier.citationPhysics Letters, Section A: General, Atomic and Solid State Physics, v. 380, n. 18-19, p. 1610-1614, 2016.
dc.identifier.doi10.1016/j.physleta.2016.02.049
dc.identifier.file2-s2.0-84961128161.pdf
dc.identifier.issn0375-9601
dc.identifier.scopus2-s2.0-84961128161
dc.identifier.urihttp://hdl.handle.net/11449/168483
dc.language.isoeng
dc.relation.ispartofPhysics Letters, Section A: General, Atomic and Solid State Physics
dc.relation.ispartofsjr0,595
dc.rights.accessRightsAcesso aberto
dc.sourceScopus
dc.subjectExtreme orbits
dc.subjectOne dimensional maps
dc.subjectParameter space
dc.titleThe role of extreme orbits in the global organization of periodic regions in parameter space for one dimensional mapsen
dc.typeArtigo
unesp.author.orcid0000-0003-1891-6415[1]

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