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Non-periodic and not everywhere dense billiard trajectories in convex polygons and polyhedrons. (English) Zbl 0529.70001


MSC:

70F99 Dynamics of a system of particles, including celestial mechanics
70G10 Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics
57R42 Immersions in differential topology
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[1] Zemlyakov, A.N., Katok, A.B.: Topological transitivity of billiards in polygons. Mat. Zametki18, 291-300 (1975) · Zbl 0315.58014
[2] Boldrighini, C., Keane, M., Marchetti, F.: Billiards in polygons. Ann. Prob.6, 532-540 (1978) · Zbl 0377.28014 · doi:10.1214/aop/1176995475
[3] Zemlyakov, A.N.: Billiards and surfaces. Kvant9, 2-9 (1979)
[4] Sinai, Ya.G.: An introduction to ergodic theory. Moscow: Erivan (Lecture 10), 1976 · Zbl 0375.28011
[5] Kornfeld, I.P., Sinai, Ya.G., Fomin, S.V.: Ergodic theory. Moscow: Nauka 1980
[6] Khinchin, A. Ya.: Continued fractions. Moscow 1961 · JFM 63.0924.02
[7] Galperin, G.A.: On systems of locally interacting and repelling particles moving in space. Trudy MMO,43, 142-196 (1981)
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