Motion close to the Hopf bifurcation of the vertical family of periodic orbits of \(L_{4}\)
type: Item
instance of: scholarly article
title: Motion close to the Hopf bifurcation of the vertical family of periodic orbits of \(L_{4}\)
zbMATH Open document ID: 1141.70005
author: Joan R. Pacha
author: Jordi Villanueva
author: M. Ollé
published in: Celestial Mechanics and Dynamical Astronomy
publication date: 2005-02-28T00:00:00Z
review text: The authors investigate the vertical family of periodic orbits of triangular points \(L_4\) and \(L_5\) in spatial circular restricted three-body problem. The authors concentrate on the case \(\mu >\mu_R\), but close to \(\mu_R\) (the Routh critical mass parameter). The motions related to the Hopf bifurcation of the vertical family which appears if the mass parameter \(\mu>\mu_R\) are considered and investigated. A special attention is paid to the family with large enough amplitudes. The authors also examine periodic orbits, 2D and 3D invariant tori, and unstable and stable invariant manifolds for hyperbolic periodic orbits.
reviewed by: Sergei Georgievich Zhuravlev
Mathematics Subject Classification ID: 70F07
Mathematics Subject Classification ID: 70K50
Mathematics Subject Classification ID: 70K42
Mathematics Subject Classification ID: 70K43
zbMATH DE Number: 2139793
zbMATH Keywords: invariant tori
zbMATH Keywords: Routh critical mass parameter
zbMATH Keywords: hyperbolic orbits
MaRDI profile type: Publication
full work available at URL: s10569-004-1592-0
OpenAlex ID: W2095179256
cites work: On the families of periodic orbits which bifurcate from the circular Sitnikov motions
cites work: Singularity theory and equivariant symplectic maps
cites work: Stability of periodic orbits in the elliptic, restricted three-body problem.
cites work: On the vertical families of two-dimensional tori near the triangular points of the bicircular problem
cites work: Periodic orbits and their bifurcations in a 3-D system
cites work: Dynamics and Mission Design Near Libration Points
cites work: Bifurcation at complex instability
cites work: Numerical computation of the normal behaviour of invariant curves of \(n\)-dimensional maps
cites work: Invariant curves near Hamiltonian–Hopf bifurcations of four-dimensional symplectic maps
cites work: Numerical computation of normal forms around some periodic orbits of the restricted three-body problem
cites work: On the normal behaviour of partially elliptic lower-dimensional tori of Hamiltonian systems
cites work: Q4511206
cites work: Dynamics close to a non semi-simple \(1:-1\) resonant periodic orbit
cites work: Q4514146
cites work: Q4251253
cites work: Three-dimensional periodic orbits about the triangular equilibrium points of the restricted problem of three bodies
DOI: 10.1007/S10569-004-1592-0
description: scientific article; zbMATH DE number 2139793