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Book Review
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Book Information
Author(s):
V. V. Kozlov and D. V. Treshchev
Title:
Billiards. A genetic introduction to the dynamics of systems with impacts
Additional book information:
Amer. Math. Soc., Providence, RI, 1991, vii+171 pp. ISBN 0-8218-4550-0
References:
- [B]
- V. Bangert, Mather sets for twist maps and geodesics on tori, Dynamics Reported \textbf{1} (1988), 1--56. MR 945963
- [Bir]
- G. D. Birkhoff, Collected mathematical papers, Vol. \RM 2, Dover, New York, 1968. MR
- [CS]
- N. I. Chernov and Ya. G. Sinai, Ergodic properties of some systems of \RM 2-dimensional discs and \RM 3-dimensional spheres, Russian Math. Surveys \textbf{42} (1987), 181--207. MR 896880
- [D]
- V. Donnay, Using integrability to produce chaos\,\RM : Billiards with positive entropy, Comm. Math. Phys. \textbf{141} (1991), 225--257. MR 1133266
- [K]
- R. Ko\l odziej, The rotation number of some transformation related to billiards in an ellipse, Studia Math. \textbf{81} (1985), 293--302. MR 808571
- [KMS]
- S. Kerckhoff, H. Masur, and J. Smillie, Ergodicity of billiard flows and quadratic differentials, Ann. of Math. (2) \textbf{124} (1986), 293--311. MR 855297
- [LW]
- C. Liverani and M. P. Wojtkowski, Ergodicity in Hamiltonian systems, Dynamics Reported. MR
- [T]
- S. Tabachnikov, Billiards, preprint, Univ. of Arkansas, 1994. MR 1328336
- [W1]
- M. P. Wojtkowski, A system of one dimensional balls with gravity, Comm. Math. Phys. \textbf{126} (1990), 507--533. MR 1032871
- [W2]
- M. P. Wojtkowski, The system of two spinning disks in the torus, Phys. D. \textbf{71} (1994), 430--439. MR 1264122
- [W3]
- M. P. Wojtkowski, Principles for the design of billiards with nonvanishing Lyapunov exponents, Comm. Math. Phys. \textbf{105} (1986), 391--414. MR 848647
- [W4]
- M. P. Wojtkowski, \emph{Systems of classical interacting particles with nonvanishing Lyapunov exponents}, Lecture Notes in Math., vol. 1486, Springer-Verlag, New York, 1991 pp.~243--262. MR 1178963
Additional Information:
Reviewer(s):
Maciej P.
Wojtkowski
Review Information:
Journal:
Bull. Amer. Math. Soc.
31
(1994),
298-301.
DOI:
10.1090/S0273-0979-1994-00537-3
PII:
S 0273-0979(1994)00537-3
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