Strange billiard tables
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- by Benjamin Halpern PDF
- Trans. Amer. Math. Soc. 232 (1977), 297-305 Request permission
Abstract:
A billiard table is any compact convex body T in the plane bounded by a continuously differentiable curve $\partial T$. An idealized billiard ball is a point which moves at unit speed in a straight line except when it hits the boundary $\partial T$ where it rebounds making the angle of incidence equal to the angle of reflection. A rather surprising phenomenon can happen on such a table.References
- George D. Birkhoff, Some unsolved problems of theoretical dynamics, Science 94 (1941), 598–600. MR 6260, DOI 10.1126/science.94.2452.598
- G. D. Birkhoff, What is the ergodic theorem?, Amer. Math. Monthly 49 (1942), 222–226. MR 6619, DOI 10.2307/2303229 —, On the periodic motions of dynamical systems, Acta Math. 50 (1927), 354-379.
- H. T. Croft and H. P. F. Swinnerton-Dyer, On the Steinhaus billiard table problem, Proc. Cambridge Philos. Soc. 59 (1963), 37–41. MR 145394, DOI 10.1017/s0305004100001961
- Konrad Knopp, Infinite sequences and series, Dover Publications, Inc., New York, 1956. Translated by Frederick Bagemihl. MR 0079110
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 232 (1977), 297-305
- MSC: Primary 58F15; Secondary 34C35
- DOI: https://doi.org/10.1090/S0002-9947-1977-0451308-7
- MathSciNet review: 0451308