Bifurcations and trifurcations of asymmetric periodic orbits

Details Bifurcations and trifurcations of asymmetric periodic orbits Bifurcations and trifurcations of asymmetric periodic orbits

Oct 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977a%26a....61..195m&link_type=abstract

Astronomy and Astrophysics, vol. 61, no. 2, Oct. 1977, p. 195-198.

Astronomy and Astrophysics

Astrophysics

9

Orbit Calculation, Three Body Problem, Algorithms, Celestial Mechanics, Solar System

Scientific paper

This paper reports on two as yet unreported features of the structure of the periodic orbits of the restricted three-body problem. These are: (1) the bifurcation of a family of asymmetric periodic orbits from another family of asymmetric periodic orbits and (2) the intersection of three different families of periodic orbits at a point of 'trifurcation'. A procedure for determining the critical values of the mass parameter of the problem for which such trifurcations occur is outlined. A number of such values are obtained, and one case exhibiting trifurcation (and bifurcation) is illustrated with concrete results.

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