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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

The symbolic representation of billiards without boundary condition


Author: Takehiko Morita
Journal: Trans. Amer. Math. Soc. 325 (1991), 819-828
MSC: Primary 58F15; Secondary 58F11, 58F22
DOI: https://doi.org/10.1090/S0002-9947-1991-1013334-6
MathSciNet review: 1013334
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Abstract: We consider a dynamical system with elastic reflections in the whole plane and show that such a dynamical system can be represented as a symbolic flow over a mixing subshift of finite type. This fact enables us to prove an analogue of the prime number theorem for the closed orbits of such a dynamical system.


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DOI: https://doi.org/10.1090/S0002-9947-1991-1013334-6
Article copyright: © Copyright 1991 American Mathematical Society