dc.contributor.author Ollé Torner, Mercè dc.contributor.author Pacha Andújar, Juan Ramón dc.contributor.author Villanueva Castelltort, Jordi dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I dc.date.accessioned 2007-05-02T16:25:57Z dc.date.available 2007-05-02T16:25:57Z dc.date.created 2003 dc.date.issued 2003 dc.identifier.uri http://hdl.handle.net/2117/840 dc.description.abstract In 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.extent 38 dc.language.iso eng dc.rights Attribution-NonCommercial-NoDerivs 2.5 Spain dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/2.5/es/ dc.subject.lcsh Bifurcation theory dc.subject.lcsh Hamiltonian systems dc.subject.other Bifurcation dc.subject.other Complex instability dc.subject.other Invariant tori dc.title Dynamics close to a non semi-simple 1: -1 resonant periodic orbit. dc.type Article dc.subject.lemac Bifurcació, Teoria de la dc.subject.lemac Hamilton, Sistemes de dc.contributor.group Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions dc.subject.ams Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems dc.subject.ams Classificació AMS::37 Dynamical systems and ergodic theory::37G Local and nonlocal bifurcation theory dc.rights.access Open Access local.personalitzacitacio true
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