Bifurcation at complex instability

Details Bifurcation at complex instability Bifurcation at complex instability

Apr 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985cemec..35..357h&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 35, April 1985, p. 357-382.

Mathematics

12

Branching (Mathematics), Orbital Mechanics, Systems Stability, Three Body Problem, Celestial Mechanics, Hamiltonian Functions

Scientific paper

In an autonomous Hamiltonian system with three or more degrees of freedom, a family of periodic orbits may become unstable when two pairs of characteristic multipliers coalesce on the unit circle at points not equal to + or - 1 and then move off the unit circle. This paper develops normal forms suitable for the neighborhood of such an instability and, at this approximation, demonstrates the bifurcation from the periodic orbit of a family of invariant two-dimensional tori. The theory is illustrated with numerical computations of orbits of the planar general three-body problem.

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