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 Títol: Dynamics close to a non semi-simple 1: -1 resonant periodic orbit. Autor: Ollé Torner, MercèPacha Andújar, Juan RamónVillanueva Castelltort, Jordi Altres autors/autores: Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions Matèries: Bifurcation theoryHamiltonian systemsBifurcationComplex instabilityInvariant toriBifurcació, Teoria de laHamilton, Sistemes de/Classificació AMS/37 Dynamical systems and ergodic theory/37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems/Classificació AMS/37 Dynamical systems and ergodic theory/37G Local and nonlocal bifurcation theory Tipus de document: Article Descripció: 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. Altres identificadors i accés: http://hdl.handle.net/2117/840 Disponible al dipòsit: E-prints UPC Comparteix:

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