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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. 相似文献
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B. S. Kruglikov 《Mathematical Notes》1997,61(2):146-163
A complete exact classification of Hamiltonian systems with Morse Hamiltonians on two-dimensional manifolds is given, i.e.,
the systems are classified up to diffeomorphisms mapping vector fields into vector fields. The classification imposes no restrictions
on Morse functions.
Translated fromMatematicheskie Zametki, Vol. 61, No. 2, pp. 179–200, February, 1997.
Translated by O. V. Sipacheva 相似文献
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