Motion close to the Hopf Bifurcation Of the vertical family of periodic orbits of L4

Details Motion close to the Hopf Bifurcation Of the vertical family of periodic orbits of L4 Motion close to the Hopf Bifurcation Of the vertical family of periodic orbits of L4

Sep 2004

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004cemda..90...87o&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 90, Issue 1-2, pp. 87-107

Astronomy and Astrophysics

Astronomy

3

Hopf Bifurcation, Invariant Manifolds, Invariant Tori, Periodic Orbits, Restricted Problem

Scientific paper

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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