On sets invariant under the action of the diagonal group

Ergodic Theory and Dynamical Systems

Volumn 21, Issue 5, 2001, Pages 1481-1500

  Lindenstrauss, Elon ^a,c   Weiss, Barak ^b,d  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

^b STONY BROOK UNIVERSITY   (United States)

^c STANFORD UNIVERSITY   (United States)

^d BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035623098     PISSN: 01433857     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0143385701001717     Document Type: Article

References (19)

1. D. V. Anosov. Geodesic flows on closed Riemannian manifolds of negative curvature. Proc. Steklov Math. Inst. 90(5) (1967).
2. D. Berend. Multi-invariant sets on Tori. Trans. Amer. Math. Soc. 280(2) (1983), 509-532.
3. A. Borel and Harish-Chandra. Arithmetic subgroups of algebraic groups. Ann. Math. 75 (1962), 485-535.
4. A. Borel and G. Prasad. Values of isotropic quadratic forms at S-integral points. Compositio Math. 83 (1992), 347-372.
5. J. W. S. Cassels and H. P. F. Swinnerton-Dyer. On the product of three homogeneous forms and indefinite ternary quadratic forms. Phil. Trans. Roy. Soc. London A 248 (1955), 73-96.
6. H. Furstenberg. Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation. Math. Sys. Theory 1 (1966), 1-49.
7. K. Hoffman and R. Kunze. Linear Algebra. Prentice Hall, Englewood Cliffs, NJ, 1961.
8. A. Katok and R. J. Spatzier. Invariant measures for higher rank hyperbolic abelian actions. Ergod. Th. & Dynam. Sys. 16 (1996), 751-778 A. Katok and R. J. Spatzier. Corrections to 'Invariant measures for higher rank hyperbolic abelian actions'. Ergod. Th. & Dynam. Sys. 18(2) (1998), 503-507.
9. A. Katok and R. J. Spatzier. Invariant measures for higher rank hyperbolic abelian actions. Ergod. Th. & Dynam. Sys. 16 (1996), 751-778 A. Katok and R. J. Spatzier. Corrections to 'Invariant measures for higher rank hyperbolic abelian actions'. Ergod. Th. & Dynam. Sys. 18(2) (1998), 503-507.
10. G. A. Margulis. Dynamical and Ergodic Properties of Subgroup Actions on Homogeneous Spaces with Applications to Number Theory (Proc. of ICM (Kyoto, 1990)). Mathematics Society of Japan and Springer, 1991, pp. 193-215.
11. G. A. Margulis. Oppenheim Conjecture (Fields Medallists' Lectures) (World Scientific Series 20th Century Mathematics, 5). World Scientific Publishing, River Edge, NJ, 1997, pp. 272-327.
12. G. A. Margulis. Problems and Conjectures in Rigidity Theory (Mathematics: Frontiers and Perspectives). American Mathematical Society, Providence, RI, 2000.
13. S. Mozes. On closures of orbits and arithmetic of quaternions. Israel J. Math. 86 (1994), 195-209.
14. V. Platonov and A. Rapinchuk. Algebraic Groups and Number Theory. Academic Press, San Diego, CA, 1994.
15. M. S. Raghunathan. Discrete Subgroups of Lie Groups. Springer, Berlin, 1972.
16. M. Ratner. Raghunathan's topological conjecture and distribution of unipotent flows. Duke J. Math. 63 (1991), 235-280.
17. P. Samuel. Algebraic Theory of Numbers. Hermann, Houghton, Mifflin, Boston, 1970.
18. N. A. Shah. Uniformly distributed orbits of certain flows on homogeneous spaces. Math. Ann. 289 (1991), 315-334.
19. R. J. Zimmer. Ergodic Theory and Semisimple Groups. Birkhäuser, Boston, 1984.