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The Kepler problem and geodesic flows in spaces of constant curvature

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Abstract

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 proceeding from the group-theory considerations. The second fact is a generalization of the theorem on structural stability of Anosov flows onto non-compact manifolds.

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Authors and Affiliations

  1. Chairperson of General Control Problems, Department of Mechanics and Mathematics, Moscow State University, U.S.S.R.

    Yu. S. Osipov

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  1. Yu. S. Osipov
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Osipov, Y.S. The Kepler problem and geodesic flows in spaces of constant curvature. Celestial Mechanics 16, 191–208 (1977). https://doi.org/10.1007/BF01228600

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  • DOI: https://doi.org/10.1007/BF01228600

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