Successive bifurcations and evolution of double and quadruple periodic orbits in the restricted three-body problem

Details Successive bifurcations and evolution of double and quadruple periodic orbits in the restricted three-body problem Successive bifurcations and evolution of double and quadruple periodic orbits in the restricted three-body problem

Mar 1987

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987a%26a...174..317p&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 174, no. 1-2, March 1987, p. 317-322.

Mathematics

4

Orbital Mechanics, Three Body Problem, Branching (Mathematics), Cartesian Coordinates, Equations Of Motion

Scientific paper

This paper investigates bifurcations of the families a, b, f, h, and n of double periodic orbits, in the restricted three body problem (case of equal masses of the primaries). In all cases infinite pitchfork period-doubling bifurcations were found, in which the Feigenbaum ratios are consistent with the universal ratio delta of about 8.72. In addition, the evolution of the families of quadruple periodic orbits bifurcating from the above families of double periodic orbits is studied. A family of quadrupole periodic orbits can have other types of bifurcations, namely bifurcations of families of nonsymmetric periodic orbits of the same period, or unstable families of symmetric eightfold periodic orbits.

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