Rigidity of measures - The high entropy case and non-commuting foliations

Israel Journal of Mathematics

Volumn 148, Issue , 2005, Pages 169-238

  Einsiedler, Manfred ^a   Katok, Anatole ^b  

^a UNIVERSITY OF WASHINGTON   (United States)

^b PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 32544452370     PISSN: 00212172     EISSN: 15658511     Source Type: Journal    
DOI: 10.1007/BF02775436     Document Type: Article

References (33)

1. D. Berend, Multi-invariant sets on tori, Transactions of the American Mathematical Society 280 (1983), 509-532.
2. D. Berend, Multi-invariant sets on compact abelian groups, Transactions of the American Mathematical Society 286 (1984), 505-535.
3. A. Borel and G. Prasad, Values of isotropic quadratic forms at S-integraJ points, Compositio Mathematica 83 (1992), 347-372.
4. N. Bourbaki, Lie groups and Lie algebras, Chapters 1-3, in Elements of Mathematics, Springer-Verlag, Berlin, 1998. Translated from the French, reprint of the 1989 English translation.
5. S. G. Dani and J. Smillie, Uniform distribution of horocycle orbits for Fuchsian groups, Duke Mathematical Journal 51 (1984), 185-194.
6. M. Einsiedler and A. Katok, Invariant measures on G/Γ for split simple Liegroups G, Communications on Pure and Applied Mathematics 56 (2003), 1184-1221.
7. M. Einsiedler, A. Katok, and E. Lindenstrauss, Invariant measures and the set of exceptions to Littlewood's conjecture, Annals of Mathematics (2), to appear.
8. d-actions on tori and solenoids, Electronic Research Announcements of the American Mathematical Society 9 (2003), 99-110.
9. M. Einsiedler and E. Lindenstrauss, Joining of semisimple actions on locally homogeneous spaces, preprint.
10. J. Feldman, A generalization of a result of R. Lyons about measures on [0,1), Israel Journal of Mathematics 81 (1993), 281-287.
11. H. Furstenberg, Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation, Mathematical Systems Theory 1 (1967), 1-49.
12. H. Furstenberg, The unique ergodicity of the horocycle flow, in Recent Advances in Topological Dynamics (Proc. Conf., Yale Univ., New Haven, Conn., 1972; in honor of Gustav Arnold Hedlund), Lecture Notes in Mathematics 318, Springer, Berlin, 1973, pp. 95-115.
13. B. Host, Nombres normaux, entropie, translations, Israel Journal of Mathematics 91 (1995), 419-428.
14. T. Hungerford, Algebra, Holt, Rinehart and Winston, New York, 1974.
15. A. S. Johnson, Measures on the circle invariant under multiplication by a nonlacunary subsemigroup of the integers, Israel Journal of Mathematics 77 (1992), 211-240.
16. B. Kalinin and A. Katok, Invariant measures for actions of higher rank abelian groups, in Smooth Ergodic Theory and its Applications (Seattle, WA, 1999), American Mathematical Society, Providence, RI, 2001, pp. 593-637.
17. B. Kalinin and R. Spatzier, Measurable rigidity for higher rank abelian actions, Ergodic Theory and Dynamical Systems 25 (2005), 175-200.
18. A. Katok and R. Spatzier, Invariant measures for higher-rank hyperbolic abelian actions, Ergodic Theory and Dynamical Systems 16 (1996), 751-778.
19. A. Katok and R. Spatzier, Corrections to: "Invariant measures for higher-rank hyperbolic abelian actions" [Ergodic Theory Dynam. Systems 16 (1996), no. 4, 751-778], Ergodic Theory and Dynamical Systems 18 (1998), 503-507.
20. F. Ledrappier and L.-S. Young, The metric entropy of diffeomorphisms. II. Relations between entropy, exponents and dimension, Annals of Mathematics (2) 122 (1985), 540-574.
21. E. Lindenstrauss, Invariant measures and arithmetic quantum unique ergodicity, Annals of Mathematics (2), to appear.
22. E. Lindenstrauss and B. Weiss, On sets invariant under the action of the diagonal group, Ergodic Theory and Dynamical Systems 21 (2001), 1481-1500.
23. R. Lyons, On measures simultaneously 2- and 3-invariant, Israel Journal of Mathematics 81 (1988), 219-224.
24. G. Margulis, Discrete subgroups and ergodic theory, in Number Theory, Trace PbrmuJas and Discrete Groups (Oslo, 1987), Academic Press, Boston, 1989, pp. 377-398.
25. G. Margulis and G. Tomanov, Invariant measures for actions of unipotent groups over local Gelds on homogeneous spaces, Inventiones Mathematicae 116 (1994), 347-392.
26. d Actions (Warwick, 1993-1994), London Mathematical Society Lecture Note Seriers, Vol. 228, Cambridge University Press, Cambridge, 1996, pp. 177-183.
27. M. Ratner, On Raghunathan's measure conjecture, Annals of Mathematics (2) 134 (1991), 545-607.
28. M. Ratner, Raghunathan's topological conjecture and distributions of unipotent flows, Duke Mathematical Journal 63 (1991), 235-280.
29. M. Ratner, Raghunathan's conjectures for SL(2, R), Israel Journal of Mathematics 80 (1992), 1-31.
30. M. Ratner, Interactions between ergodic theory, Lie groups, and number theory, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994), Birkhäuser, Basel, 1995, pp. 157-182.
31. M. Ratner, Raghunathan's conjectures for Cartesian products of real and p-adic Lie groups, Duke Mathematical Journal 77 (1995), 275-382.
32. 2-Anosov flows, Unpublished manuscript, 1982.
33. D. J. Rudolph, ×2 and ×3 invariant measures and entropy, Ergodic Theory and Dynamical Systems 10 (1990), 395-406.