Summary
In an elliptical billiard there exists, in contrast to a circular one, an exception toPoincaré's recurrence theorem, in as much as the path of a billiard-ball that goes through a focus of the ellipse converges toward the long axis.
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Literatur
H. Poincaré, Les méthodes nouvelles de la mécanique céleste, t. 3, chap. 26, p. 140 ff.
J. Hadamard, J. Math., 5e sér.3, 331 (1897).
C. Carathéodory, Sitzungsber. der Preuß. Akad. (1919), 2. Halbbd., p. 580 ff.
G. D. Birkhoff, Dynamical Systems (1927), p. 251.
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Batschelet, E. Über einen Ausnahmefall des Wiederkehrsatzes von Poincaré. Experientia 4, 270 (1948). https://doi.org/10.1007/BF02164403
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DOI: https://doi.org/10.1007/BF02164403