The Kepler problem and geodesic flows in spaces of constant curvature

Details The Kepler problem and geodesic flows in spaces of constant curvature The Kepler problem and geodesic flows in spaces of constant curvature

Oct 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977cemec..16..191o&link_type=abstract

Celestial Mechanics, vol. 16, Oct. 1977, p. 191-208.

Computer Science

8

Celestial Mechanics, Geodesic Lines, Kepler Laws, Flow Stability, Lie Groups

Scientific paper

The main result of this paper is a theorem on the trajectory equivalence of phase flows on isoenergetic surfaces with a positive energy level in the Kepler problem and perturbed Kepler problem. The following two facts are crucial for proving it: firstly, an isomorphism of the phase flow on an isoenergetic surface in the Kepler problem and the geodesic flow in a constant curvature space. The isomorphism is studied in detail. In particular, all the integrals of the Kepler problem are obtained from the group-theoretical considerations. The second fact is a generalization of the theorem on structural stability of Anosov flows onto noncompact manifolds.

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