Topology of billiard problems, I

Duke Mathematical Journal

Volumn 115, Issue 3, 2002, Pages 559-585

  Farber, Michael ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036926175     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-02-11535-X     Document Type: Article

References (18)

1. D.V. Anosov, Some homotopies in a space of closed curves, Math. USSR-Izv. 17 (1981), 423 - 453. MR 83i:58028.
2. I. Babenko, Periodic trajectories of three-dimensional Birkhoff billiards, Math. USSR-Sb. 71, no. 1 (1992), 1 - 13. MR 91m:58128.
3. G. Birkhoff, Dynamical Systems, Amer. Math. Soc. Colloq. Publ. 9, Amer. Math. Soc., Providence, 1966. MR 35:1.
4. A. Borel, Seminar on Transformation Groups, Ann. of Math. Stud. 46, Princeton Univ. Press, Princeton, 1960. MR 22:7129.
5. R. Bott, The stable homotopy of the classical groups, Ann. of Math. (2) 70 (1959), 313 - 337. MR 22:987.
6. _, Lectures on Morse theory, old and new, Bull. Amer. Math. Soc. (N.S.) 7 (1982), 331 - 358. MR 84m:58026a.
7. F. Cohen, "Artin's braid groups, classical homotopy theory, and sundry other curiosities" in Braids (Santa Cruz, Calif., 1986), Contemp. Math. 78, Amer. Math. Soc., Providence, 1988, 167 - 206. MR 90a:20077.
8. _, On configuration spaces, their homology, and Lie algebras, J. Pure Appl. Algebra 100 (1995), 19 - 42. MR 96d:55005.
9. H. Croft and H. Swinnerton-Dyer, On the Steinhaus billiard table problem, Proc. Cambridge Philos. Soc. 59 (1963), 37 - 41. MR 26:2925.
10. M. Farber and S. Tabachnikov, Topology of cyclic configuration spaces and periodic trajectories of multi-dimensional billiards, Topology 41 (2002), 553 - 589. CMP 1 910 041.
11. J. Jost, Riemannian Geometry and Geometric Analysis, Universitext, Springer, Berlin, 1995. MR 96g:53049.
12. W. Klingenberg, Lectures on Closed Geodesics, Grundlehren Math. Wiss. 230, Springer, Berlin, 1978. MR 57:17563.
13. V.V. Kozlov and D.V. Treshchev, Billiards: A Genetic Introduction to the Dynamics of Systems with Impacts, Transl. Math. Monogr. 89, Amer. Math. Soc., Providence, 1991. MR 93k:58094a.
14. J. Milnor, Morse Theory, Ann. of Math. Stud. 51, Princeton Univ. Press, Princeton, 1973. MR 29:634.
15. M. Morse and E. Baiada, Homotopy and homology related to the Schoenflies problem, Ann. of Math. (2) 58 (1953), 142 - 165. MR 15:146g.
16. J.-P. Serre, Homologie singulière des espaces fibrés: Applications, Ann. of Math. (2) 54 (1951), 425 - 505. MR 13:574g.
17. S. Tabachnikov, Billiards, Panor. Synth. 1, Soc Math. France, Montrouge, 1995. MR 96c:58134.
18. B. Totaro, Configuration spaces of algebraic varieties, Topology 35 (1996), 1057-1067. MR 97g:57033.