Book Review
The AMS does not provide abstracts of book reviews.
You may download the entire review from the links below.
MathSciNet review:
1118378
Full text of review:
PDF
This review is available free of charge.
Book Information:
Author:
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.
V. Bangert, Mather sets for twist maps and geodesics on tori, Dynamics reported, Vol. 1, Dynam. Report. Ser. Dynam. Systems Appl., vol. 1, Wiley, Chichester, 1988, pp. 1–56. MR 945963
[Bir] G. D. Birkhoff, Collected mathematical papers, Vol. 2, Dover, New York, 1968.
Ya. G. Sinaĭ and N. I. Chernov, Ergodic properties of some systems of two-dimensional disks and three-dimensional balls, Uspekhi Mat. Nauk 42 (1987), no. 3(255), 153–174, 256 (Russian). MR 896880
Victor J. Donnay, Using integrability to produce chaos: billiards with positive entropy, Comm. Math. Phys. 141 (1991), no. 2, 225–257. MR 1133266
RafałKołodziej, The rotation number of some transformation related to billiards in an ellipse, Studia Math. 81 (1985), no. 3, 293–302. MR 808571, DOI 10.4064/sm-81-3-293-302
Steven Kerckhoff, Howard Masur, and John Smillie, Ergodicity of billiard flows and quadratic differentials, Ann. of Math. (2) 124 (1986), no. 2, 293–311. MR 855297, DOI 10.2307/1971280
Carlangelo Liverani and Maciej P. Wojtkowski, Ergodicity in Hamiltonian systems, Dynamics reported, Dynam. Report. Expositions Dynam. Systems (N.S.), vol. 4, Springer, Berlin, 1995, pp. 130–202. MR 1346498
Serge Tabachnikov, Billiards, Panor. Synth. 1 (1995), vi+142 (English, with English and French summaries). MR 1328336
Maciej P. Wojtkowski, A system of one-dimensional balls with gravity, Comm. Math. Phys. 126 (1990), no. 3, 507–533. MR 1032871
Maciej P. Wojtkowski, The system of two spinning disks in the torus, Phys. D 71 (1994), no. 4, 430–439. MR 1264122, DOI 10.1016/0167-2789(94)90009-4
Maciej Wojtkowski, Principles for the design of billiards with nonvanishing Lyapunov exponents, Comm. Math. Phys. 105 (1986), no. 3, 391–414. MR 848647
Maciej P. Wojtkowski, Systems of classical interacting particles with nonvanishing Lyapunov exponents, Lyapunov exponents (Oberwolfach, 1990) Lecture Notes in Math., vol. 1486, Springer, Berlin, 1991, pp. 243–262. MR 1178963, DOI 10.1007/BFb0086674
- [B]
- V. Bangert, Mather sets for twist maps and geodesics on tori, Dynamics Reported 1 (1988), 1-56. MR 945963 (90a:58145)
- [Bir]
- G. D. Birkhoff, Collected mathematical papers, Vol. 2, Dover, New York, 1968.
- [CS]
- N. I. Chernov and Ya. G. Sinai, Ergodic properties of some systems of 2-dimensional discs and 3-dimensional spheres, Russian Math. Surveys 42 (1987), 181-207. MR 896880 (89c:58097)
- [D]
- V. Donnay, Using integrability to produce chaos: Billiards with positive entropy, Comm. Math. Phys. 141 (1991), 225-257. MR 1133266 (93c:58111)
- [K]
- R. Kołodziej, The rotation number of some transformation related to billiards in an ellipse, Studia Math. 81 (1985), 293-302. MR 808571 (87b:58048)
- [KMS]
- S. Kerckhoff, H. Masur, and J. Smillie, Ergodicity of billiard flows and quadratic differentials, Ann. of Math. (2) 124 (1986), 293-311. MR 855297 (88f:58122)
- [LW]
- C. Liverani and M. P. Wojtkowski, Ergodicity in Hamiltonian systems, Dynamics Reported (to appear). MR 1346498 (96g:58144)
- [T]
- S. Tabachnikov, Billiards, preprint, Univ. of Arkansas, 1994. MR 1328336 (96c:58134)
- [W1]
- M. P. Wojtkowski, A system of one dimensional balls with gravity, Comm. Math. Phys. 126 (1990), 507-533. MR 1032871 (91h:58066)
- [W2]
- -, The system of two spinning disks in the torus, Phys. D. 71 (1994), 430-439. MR 1264122 (95a:58105)
- [W3]
- -, Principles for the design of billiards with nonvanishing Lyapunov exponents, Comm. Math. Phys. 105 (1986), 391-414. MR 848647 (87k:58165)
- [W4]
- -, Systems of classical interacting particles with nonvanishing Lyapunov exponents, Lyapunov Exponents, Proceedings, Oberwolfach 1990 (L. Arnold, H. Crauel, and J.-P. Eckmann, eds.), Lecture Notes in Math., vol. 1486, Springer-Verlag, New York, 1991, pp. 243-262. MR 1178963 (93g:58088)
Review Information:
Reviewer:
Maciej P. Wojtkowski
Journal:
Bull. Amer. Math. Soc.
31 (1994), 298-301
DOI:
https://doi.org/10.1090/S0273-0979-1994-00537-3
