Distribution rigidity for unipotent actions on homogeneous spaces
Author:
Marina Ratner
Journal:
Bull. Amer. Math. Soc. 24 (1991), 321325
MSC (1985):
Primary 22E40
MathSciNet review:
1069988
Fulltext PDF
References  Similar Articles  Additional Information
 Frederick P. Greenleaf and William R. Emerson, Group structure and the pointwise ergodic theorem for connected amenable groups, Advances in Math. 14 (1974), 153–172. MR 0384997
 S. G. Dani, Invariant measures and minimal sets of horospherical flows, Invent. Math. 64 (1981), no. 2, 357–385. MR 629475, 10.1007/BF01389173
 S. G. Dani and John Smillie, Uniform distribution of horocycle orbits for Fuchsian groups, Duke Math. J. 51 (1984), no. 1, 185–194. MR 744294, 10.1215/S001270948405110X
 S. G. Dani and G. A. Margulis, Orbit closures of generic unipotent flows on homogeneous spaces of 𝑆𝐿(3,𝑅), Math. Ann. 286 (1990), no. 13, 101–128. MR 1032925, 10.1007/BF01453567
 H. Furstenberg, Strict ergodicity and transformation of the torus, Amer. J. Math. 83 (1961), 573–601. MR 0133429
 Harry Furstenberg, The unique ergodicity of the horocycle flow, Recent advances in topological dynamics (Proc. Conf., Yale Univ., New Haven, Conn., 1972; in honor of Gustav Arnold Hedlund), Springer, Berlin, 1973, pp. 95–115. Lecture Notes in Math., Vol. 318. MR 0393339
 G. A. Margulis, Discrete subgroups and ergodic theory, Number theory, trace formulas and discrete groups (Oslo, 1987) Academic Press, Boston, MA, 1989, pp. 377–398. MR 993328
 Donald S. Ornstein and Benjamin Weiss, Entropy and isomorphism theorems for actions of amenable groups, J. Analyse Math. 48 (1987), 1–141. MR 910005, 10.1007/BF02790325
 William Parry, Ergodic properties of affine transformations and flows on nilmanifolds., Amer. J. Math. 91 (1969), 757–771. MR 0260975
 Marina Ratner, Strict measure rigidity for unipotent subgroups of solvable groups, Invent. Math. 101 (1990), no. 2, 449–482. MR 1062971, 10.1007/BF01231511
 Marina Ratner, On measure rigidity of unipotent subgroups of semisimple groups, Acta Math. 165 (1990), no. 34, 229–309. MR 1075042, 10.1007/BF02391906

[R3] M. Ratner, On Raghunathan's measure conjecture, Ann. of Math, (to appear).
 Marina Ratner, Horocycle flows, joinings and rigidity of products, Ann. of Math. (2) 118 (1983), no. 2, 277–313. MR 717825, 10.2307/2007030
 Dave Witte, Rigidity of some translations on homogeneous spaces, Invent. Math. 81 (1985), no. 1, 1–27. MR 796188, 10.1007/BF01388769
Retrieve articles in Bulletin of the American Mathematical Society with MSC (1985): 22E40
Retrieve articles in all journals with MSC (1985): 22E40
Additional Information
DOI:
https://doi.org/10.1090/S027309791991160222