The geodesic flow on a two-dimensional ellipsoid in the field of an elastic force. Topological classification of solutions

DOI10.3103/S0027132218020031zbMath1433.70010WikidataQ129903325 ScholiaQ129903325MaRDI QIDQ1795422

I. F. Kobtsev

Publication date: 16 October 2018

Published in: Moscow University Mathematics Bulletin (Search for Journal in Brave)

Mathematics Subject Classification ID

Geodesic flows in symplectic geometry and contact geometry (53D25) Motion of a rigid body in contact with a solid surface (70E18) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

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Cites Work

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• Each finite group is the symmetry group of some map (an ``atom-bifurcation)
• The Chaplygin case in dynamics of a rigid body in fluid is orbitally equivalent to the Euler case in rigid body dynamics and to the Jacobi problem about geodesics on the ellipsoid
• Some integrable extensions of Jacobi's problem of geodesics on an ellipsoid
• Topological classification of the Goryachev integrable systems in the rigid body dynamics: non-compact case

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