A topological classification of integrable geodesic flows on the two-dimensional sphere with an additional integral quadratic in the momenta |
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Authors: | T Z Nguyen L S Polyakova |
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Institution: | (1) Department of Differential Geometry and Applications, Faculty of Mathematics and Mechanics, Moscow State University, 119899 Moscow, Russia |
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Abstract: | Summary The analytic expression for a Riemannian metric on a 2-sphere, having integrable geodesic flow with an additional integral
quadratic in momenta, is given in Ko1]. We give the topological classification, up to topological equivalence of Liouville
foliations, of all such metrics. The classification is computable, and the formula for calculating the complexity of the flow
is straightforward. We prove Fomenko's conjecture that, from the point of view of complexity, the integrable geodesic flows
with an additional integral linear or quadratic in momenta exhaust “almost all” integrable geodesic flows on the 2-dimensional
sphere. |
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Keywords: | integrable system Hamiltonian system topological equivalence geodesic flow letter-atom word-molecule |
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