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

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 equi...

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Detalles Bibliográficos
Autores: Ollé Torner, Mercè|||0000-0002-8050-9055, Pacha Andújar, Juan Ramón|||0000-0003-4599-3141, Villanueva Castelltort, Jordi|||0000-0001-8725-2785
Tipo de recurso: artículo
Fecha de publicación:2003
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/1203
Acceso en línea:https://hdl.handle.net/2117/1203
Access Level:acceso abierto
Palabra clave: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
Descripción
Sumario: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.

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