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- W2953680480 endingPage "1173" @default.
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- W2953680480 abstract "Abstract The authors have recently introduced the class of topological billiards. Topological billiards are glued from elementary planar billiard sheets (bounded by arcs of confocal quadrics) along intervals of their boundaries. It turns out that the integrability of the elementary billiards implies that of the topological billiards. We show that all classical linearly and quadratically integrable geodesic flows on tori and spheres are Liouville equivalent to appropriate topological billiards. Moreover, the linear and quadratic integrals of the geodesic flows reduce to a single canonical linear integral and a single canonical quadratic integral on the billiard. These results are obtained within the framework of the Fomenko–Zieschang theory of the classification of integrable systems." @default.
- W2953680480 created "2019-07-12" @default.
- W2953680480 creator A5034334425 @default.
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- W2953680480 date "2019-12-01" @default.
- W2953680480 modified "2023-10-13" @default.
- W2953680480 title "Integrable geodesic flows on orientable two-dimensional surfaces and topological billiards" @default.
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- W2953680480 doi "https://doi.org/10.1070/im8863" @default.
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