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Topological classification of quadratic-integrable geodesic flows on a two-dimensional torus. (English. Russian original) Zbl 0992.37501
Russ. Math. Surv. 50, No. 1, 200-201 (1995); translation from Usp. Mat. Nauk 50, No. 1, 201-202 (1995).
Using the enumeration of all the square-integrable geodesic flows on the two-torus obtained by I. K. Babenko and N. N. Nekhoroshev (and their constructions of suitable metrics on the torus), the author finds the explicit form of the word-molecule (Fomenko-Zieschang invariant) of a square-integrable geodesic flow on \(T^2\). His technique is based in an essential way on the results of Nguyen Tien Zung, L. S. Polyakova and E. N. Selivanova [Funct. Anal. Appl. 27, No. 3, 186-196 (1993); translation from Funkts. Anal. Prilozh. 27, No. 3, 42-56 (1993; Zbl 0804.58042)].
Reviewer: J.S.Joel (Kelly)

MSC:
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
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