Motion close to the hopf bifurcation of the vertical family of periodic orbits of L^4

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To access the full text documents, please follow this link: http://hdl.handle.net/2117/1203

Title:	Motion close to the hopf bifurcation of the vertical family of periodic orbits of L^4
Author:	Ollé Torner, Mercè; Pacha Andújar, Juan Ramón; Villanueva Castelltort, Jordi
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
Abstract:	The paper deals with diﬀerent kinds of invariant motions (periodic orbits, 2D and 3D invariant tori and invariant manifolds of periodic orbits) in order to analyze the Hamiltonian direct Hopf bifurcation that takes place close to the Lyapunov vertical family of periodic orbits of the triangular equilibrium point L4 in the 3D restricted three-body problem (RTBP) for the mass parameter, µ, greater than (and close to) µR (Routh’s mass parameter). Consequences of such bifurcation, concerning the conﬁnement of the motion close to the hyperbolic orbits and the 3D nearby tori are also described.
Subject(s):	-Hamiltonian systems -Differentiable dynamical systems -Dynamics -Hamiltonian dynamical systems -Lagrangian functions -restricted problem -periodic orbits -Hopf bifurcation -invariant tori -invariant manifolds -Hamilton, Sistemes de -Sistemes dinàmics diferenciables -Teoria ergòdica -Partícules (Física nuclear) -Lagrange, Funcions 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::37N Applications -Classificació AMS::70 Mechanics of particles and systems::70F Dynamics of a system of particles, including celestial mechanics -Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics
Rights:	Attribution-NonCommercial-NoDerivs 2.5 Spain http://creativecommons.org/licenses/by-nc-nd/2.5/es/
Document type:	Article
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