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dc.contributor.authorOllé Torner, Mercè
dc.contributor.authorPacha Andújar, Juan Ramón
dc.contributor.authorVillanueva Castelltort, Jordi
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.date.accessioned2007-05-02T16:25:57Z
dc.date.available2007-05-02T16:25:57Z
dc.date.created2003
dc.date.issued2003
dc.identifier.urihttp://hdl.handle.net/2117/840
dc.description.abstractIn this work, our target is to analyze the dynamics around the $1:-1$ resonance which appears when a family of periodic orbits of a real analytic three-degree of freedom Hamiltonian system changes its stability from elliptic to a complex hyperbolic saddle passing through degenerate elliptic. Our analytical approach consists of computing, in a constructive way and up to some given arbitrary order, the normal form around that resonant (or \emph{critical}) periodic orbit. Hence, dealing with the normal form itself and the differential equations related to it, we derive the generic existence of a two-parameter family of invariant 2D tori which bifurcate from the critical periodic orbit. Moreover, the coefficient of the normal form that determines the stability of the bifurcated tori is identified. This allows us to show the Hopf-like character of the unfolding: elliptic tori unfold ``around'' hyperbolic periodic orbits (case of \emph{direct} bifurcation) while normal hyperbolic tori appear ``around'' elliptic periodic orbits (case of \emph{inverse} bifurcation). Further, a global description of the dynamics of the normal form is also given.
dc.format.extent38
dc.language.isoeng
dc.rightsAttribution-NonCommercial-NoDerivs 2.5 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/2.5/es/
dc.subject.lcshBifurcation theory
dc.subject.lcshHamiltonian systems
dc.subject.otherBifurcation
dc.subject.otherComplex instability
dc.subject.otherInvariant tori
dc.titleDynamics close to a non semi-simple 1: -1 resonant periodic orbit.
dc.typeArticle
dc.subject.lemacBifurcació, Teoria de la
dc.subject.lemacHamilton, Sistemes de
dc.contributor.groupUniversitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
dc.subject.amsClassificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
dc.subject.amsClassificació AMS::37 Dynamical systems and ergodic theory::37G Local and nonlocal bifurcation theory
dc.rights.accessOpen Access
local.personalitzacitaciotrue


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