Invariant measures and stiffness for non-Abelian groups of toral automorphisms

Comptes Rendus Mathematique

Volumn 344, Issue 12, 2007, Pages 737-742

  Bourgain, Jean ^a   Furman, Alex ^b   Lindenstrauss, Elon ^c   Mozes, Shahar ^d  

^a INSTITUTE FOR ADVANCED STUDY   (United States)

^b UNIVERSITY OF ILLINOIS AT CHICAGO   (United States)

^c PRINCETON UNIVERSITY   (United States)

^d HEBREW UNIVERSITY OF JERUSALEM   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34447341450     PISSN: 1631073X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.crma.2007.04.017     Document Type: Article

References (21)

1. Berend D. Multi-invariant sets on tori. Trans. Amer. Math. Soc. 280 2 (2000) 509-532
2. Bougerol P., and Lacroix J. Products of Random Matrices with Applications to Schrödinger Operators (1985), Birkhäuser
3. Bourgain J. On the Erdös-Volkmann and Katz-Tao ring conjecture. GAFA 13 (2003) 334-365
4. J. Bourgain, A. Gamburd, On the spectral gap for finitely-generated subgroups of SU (2), preprint, Invent., submitted for publication
5. d-actions on tori and solenoids. Electron. Res. Announc. Amer. Math. Soc. 9 (2003) 99-110
6. Furstenberg H. Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation. Math. Systems Theory 1 (1967) 1-49
7. Furstenberg H. Stiffness of group actions. Lie Groups and Ergodic Theory. Mumbai, 1996. Tata Inst. Fund. Res. Stud. Math. vol. 14 (1998), Tata Inst. Fund. Res., Bombay 105-117
8. Gol'dsheǐd I.Ya., and Margulis G.A. Lyapunov exponents of a product of random matrices. Uspekhi Mat. Nauk 44 5(269) (1989) 13-60 (in Russian). Translation in
9. Gol'dsheǐd I.Ya., and Margulis G.A. Lyapunov exponents of a product of random matrices. Russian Math. Surveys 44 5 (1989) 11-71
10. Y. Guivarc'h, private communication
11. Guivarc'h Y., and Starkov A.N. Orbits of linear group actions, random walk on homogeneous spaces, and toral automorphisms. Ergodic Theory Dynam. Systems 24 3 (2004) 767-802
12. Kalinin B., and Katok A. Invariant measures for actions of higher rank abelian groups. Smooth Ergodic Theory and its Applications. Seattle, WA, 1999. Proc. Sympos. Pure Math. vol. 69 (2001), Amer. Math. Soc. Providence, RI 593-637
13. Katok A., and Spatzier R. Invariant measures for higher rank hyperbolic abelian actions. Ergodic Theory Dynam. Systems 16 4 (1996) 751-778
14. Katz N., and Tao T. Some connections between Falconer's distance set conjecture and sets of Furstenberg type. New York J. Math. 7 (2001) 149-187
15. Margulis G.A. Problems and conjectures in rigidity theory. Mathematics: Frontiers and Perspectives (2000), Amer. Math. Soc. 161-174
16. R. Muchnik, Orbits of Zariski dense semigroups of SL (n, Z), Ergodic Theory Dynam. Systems
17. n. Geom. Dedicata 110 (2005) 1-47
18. Pink R. Strong approximation for Zariski dense subgroups over arbitrary global fields. Comment. Math. Helv. 75 4 (2000) 608-643
19. Rudolph D. ×2 and ×3 invariant measures and entropy. Ergodic Theory Dynam. Systems 10 2 (1990) 395-406
20. A.N. Starkov, Orbit closures of toral automorphism groups, preprint, Moscow, 1999
21. Weisfeiler B. Strong approximation for Zariski-dense subgroups of semisimple algebraic groups. Ann. of Math. (2) 120 2 (1984) 271-315