Invariant curves near Hamiltonian-Hopf bifurcations of 4D symplectic maps

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To access the full text documents, please follow this link: http://hdl.handle.net/2117/1222

dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.contributor	Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
dc.contributor.author	Jorba, Angel
dc.contributor.author	Ollé Torner, Mercè
dc.date	2003
dc.identifier.uri	http://hdl.handle.net/2117/1222
dc.language.iso	eng
dc.rights	Attribution-NonCommercial-NoDerivs 2.5 Spain
dc.rights	info:eu-repo/semantics/openAccess
dc.rights	http://creativecommons.org/licenses/by-nc-nd/2.5/es/
dc.subject	Hamiltonian systems
dc.subject	Differentiable dynamical systems
dc.subject	complex instability
dc.subject	invariant curves
dc.subject	invariant manifolds
dc.subject	Hamilton, Sistemes de
dc.subject	Sistemes dinàmics diferenciables
dc.subject	Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
dc.subject	Classificació AMS::37 Dynamical systems and ergodic theory::37M Approximation methods and numerical treatment of dynamical systems
dc.title	Invariant curves near Hamiltonian-Hopf bifurcations of 4D symplectic maps
dc.type	info:eu-repo/semantics/article
dc.description.abstract	In this paper we give a numerical description of the neighbourhood of a fixed point of a symplectic map undergoing a transition from linear stability to complex instability, i.e., the so called Hamiltonian-Hopf bifurcation. We have considered both the direct and inverse cases. The study is based on the numerical computation of the Lyapunov families of invariant curves near the fixed point. We show how these families, jointly with their invariant manifolds and the invariant manifolds of the fixed point organise the phase space around the bifurcation.

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