On the existence of periodic orbits and KAM tori in the Sprott A system: a special case of the Nosé–Hoover oscillator

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dc.contributor.authorMessias, Marcelo [UNESP]
dc.contributor.authorReinol, Alisson C. [UNESP]
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.date.accessioned2018-12-11T17:17:59Z
dc.date.available2018-12-11T17:17:59Z
dc.date.issued2018-05-01
dc.description.abstractWe consider the well-known Sprott A system, which is a special case of the widely studied Nosé–Hoover oscillator. The system depends on a single real parameter a, and for suitable choices of the parameter value, it is shown to present chaotic behavior, even in the absence of an equilibrium point. In this paper, we prove that, for a≠ 0 , the Sprott A system has neither invariant algebraic surfaces nor polynomial first integrals. For a> 0 small, by using the averaging method we prove the existence of a linearly stable periodic orbit, which bifurcates from a non-isolated zero-Hopf equilibrium point located at the origin. Moreover, we show numerically the existence of nested invariant tori surrounding this periodic orbit. Thus, we observe that these dynamical elements and their perturbation play an important role in the occurrence of chaotic behavior in the Sprott A system.en
dc.description.affiliationDepartamento de Matemática e Computação Faculdade de Ciências e Tecnologia Universidade Estadual Paulista (UNESP)
dc.description.affiliationDepartamento de Matemática Instituto de Biociências Letras e Ciências Exatas Universidade Estadual Paulista (UNESP)
dc.description.affiliationUnespDepartamento de Matemática e Computação Faculdade de Ciências e Tecnologia Universidade Estadual Paulista (UNESP)
dc.description.affiliationUnespDepartamento de Matemática Instituto de Biociências Letras e Ciências Exatas Universidade Estadual Paulista (UNESP)
dc.format.extent1287-1297
dc.identifierhttp://dx.doi.org/10.1007/s11071-018-4125-1
dc.identifier.citationNonlinear Dynamics, v. 92, n. 3, p. 1287-1297, 2018.
dc.identifier.doi10.1007/s11071-018-4125-1
dc.identifier.file2-s2.0-85042069964.pdf
dc.identifier.issn1573-269X
dc.identifier.issn0924-090X
dc.identifier.lattes3757225669056317
dc.identifier.scopus2-s2.0-85042069964
dc.identifier.urihttp://hdl.handle.net/11449/175881
dc.language.isoeng
dc.relation.ispartofNonlinear Dynamics
dc.rights.accessRightsAcesso aberto
dc.sourceScopus
dc.subjectAveraging method
dc.subjectChaotic behavior
dc.subjectInvariant algebraic surfaces
dc.subjectNested invariant tori
dc.subjectNosé–Hoover oscillator
dc.subjectPeriodic orbits
dc.subjectSprott A system
dc.titleOn the existence of periodic orbits and KAM tori in the Sprott A system: a special case of the Nosé–Hoover oscillatoren
dc.typeArtigo
unesp.author.lattes3757225669056317

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Artigos - Matemática e Computação - FCT
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