Algorithms, Fractals, and Dynamics pp 169-177 | Cite as
On the Length Spectrum of the Bounded Scattering Billiards Table
Chapter
Abstract
Let Q be a bounded connected plane domain with piecewise smooth boundary ∂Q.
Keywords
Periodic Point Closed Orbit Collision Time Discrete Dynamical System Incidental Vector
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
References
- [B.S.C]L. A. Bunimovich, Ya. G. Sinai, and N. J. Chernov, Markov partitions for two-dimensional hyperbolic billiards, Russian Math. Surveys 45, (1990), 105–152.MathSciNetMATHCrossRefGoogle Scholar
- [C.F.S]I. P. Cornfeld, S. V. Formin, and Ya. G. Sinai, Ergodic theory, Springer, New York. (1982)MATHGoogle Scholar
- [E]B. Eckhardt, Periodic orbit theory, preprintGoogle Scholar
- [G]M. C. Gutzwiller, Chaos in classical and quantum mechanics, Springer, New York. (1990).MATHGoogle Scholar
- [I]M. Ikawa, Singular perturbation of symbolic flows and poles of the zeta functions, Osaka J. Math., 27, (1990), 281–300.MathSciNetMATHGoogle Scholar
- [M]T. Morita, The symbolic representation of billiards without boundary condition, Trans. Amer. Math. Soc. 325, (1989), 819–828.CrossRefGoogle Scholar
- [P.P]W. Parry and M. Pollicott, An analogue of the prime number theorem for closed orbits of Axiom A flows, Ann. of Math. 118, (1983), 573– 591.MathSciNetMATHCrossRefGoogle Scholar
- [S]Ya. G. Sinai, Dynamical systems with elastic reflections, Russian Math. Surveys, 25, (1970), 137–189.MathSciNetMATHCrossRefGoogle Scholar
- [St]L. Stojanov, An estimate from above of the number of periodic orbits for semi-newline dispersed billiards, Common. Math. Phys. 124, (1989), 217–227.MathSciNetMATHCrossRefGoogle Scholar
Copyright information
© Plenum Press, New York 1995