Bifurcations, stability and universality of families of periodic orbits in the restricted three-body problem

Details Bifurcations, stability and universality of families of periodic orbits in the restricted three-body problem Bifurcations, stability and universality of families of periodic orbits in the restricted three-body problem

Apr 1986

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986a%26a...159..231p&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 159, no. 1-2, April 1986, p. 231-238.

Mathematics

4

Celestial Mechanics, Dynamic Stability, Orbit Perturbation, Three Body Problem, Branching (Mathematics), Period Doubling

Scientific paper

The author studies some bifurcations of the main families of simple periodic orbits a, b, c, f, g, h, i, k and l of the restricted three-body problem in the case of equal masses of the primaries. There are several cases of infinite pitchfork period-doubling bifurcations, in which the bifurcation ratio is consistent with the universal ratio δ ≅ 8.72. But the author found also cases of bifurcations of unstable families of periodic orbits, which do not present infinite period doubling bifurcations. He followed the evolution of the families of double periodic orbits bifurcating from the above families.

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