Mathematics
Scientific paper
Oct 1983
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983cemec..31..193c&link_type=abstract
Celestial Mechanics (ISSN 0008-8714), vol. 31, Oct. 1983, p. 193-211.
Mathematics
12
Barred Galaxies, Celestial Mechanics, Galactic Rotation, Orbit Perturbation, Orbital Mechanics, Branching (Mathematics), Degrees Of Freedom, Galactic Evolution, Period Doubling, Resonance, Systems Stability, Three Body Problem
Scientific paper
The various families of periodic orbits in a dynamical system representing a plane rotating barred galaxy are studied. A general view of the main resonant types of orbits can be obtained by considering the axisymmetric background. The introduction of a bar perturbation produces infinite gaps along the central family x1 (the family of circular orbits in the axisymmetric case). It produces also higher order bifurcations, unstable regions along the family x1, and long period orbits around L4 and L5. The evolution of the various types of orbits is described, as the Jacobi constant h and the bar amplitude increase. Of special importance are the infinities of period doubling pitchfork bifurcations. The genealogy of the long and short period orbits is described in detail. There are infinite gaps along the long period orbits producing an infinity of families. All of them bifurcate from the short period family. The rules followed by these families are described. Also an infinity of higher order bridges join the short and long period families. The analogies with the restricted three body problem are stressed.
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