Bulletin (New Series) of the American Mathematical Society

Distribution rigidity for unipotent actions on homogeneous spaces

Marina Ratner

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Bull. Amer. Math. Soc. (N.S.), Volume 24, Number 2 (1991), 321-325.

First available in Project Euclid: 5 July 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 22E40: Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx]


Ratner, Marina. Distribution rigidity for unipotent actions on homogeneous spaces. Bull. Amer. Math. Soc. (N.S.) 24 (1991), no. 2, 321--325. https://projecteuclid.org/euclid.bams/1183656870

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  • [GE] P. Greenleaf and W. R. Emerson, Group structure and pointwise ergodic theorem for connected amenable groups, Adv. in Math. 14 (1974), 153-172.
  • [D1] S. G. Dani, Invariant measures and minimal sets of horospherical flows, Invent. Math. 64 (1981), 357-385.
  • [DS] S. G. Dani and J. Smillie, Uniform distribution of horocycle orbits for Fuchsian groups, Duke Math. J. 51 (1984), 185-194.
  • [DM] S. G. Dani and G. A. Margulis, Orbit closures of generic unipotent flows on homogeneous spaces of SL(3, R), Math. Ann. 286 (1990), 101-128..
  • [F1] H. Furstenberg, Strict ergodicity and transformations of the torus, Amer. J. Math. 83 (1961), 573-601.
  • [F2] H. Furstenberg, The unique ergodicity of the horocycle flow, Recent Advances in Topological Dynamics, Springer-Verlag, Berlin and New York, 1972, pp. 95-115.
  • [M] G. A. Margulis, Discrete subgroups and ergodic theory, Proc. Conf. in Honor of A. Selberg, 1989, Oslo.
  • [OW] D. Ornstein and B. Weiss, Entropy and isomorphism theorems for actions of amenable groups, J. Analyse Math. 48 (1987), 1-140.
  • [P] W. Parry, Ergodic properties of affine transformations and flows on nilmanifolds, Amer. J. Math. 91 (1969), 757-771.
  • [R1] M. Ratner, Strict measure rigidity for unipotent subgroups of solvable groups, Invent. Math. 101 (1990), 449-482.
  • [R2] M. Ratner, On measure rigidity of unipotent subgroups of semisimple groups, Acta Math, (to appear).
  • [R3] M. Ratner, On Raghunathan's measure conjecture, Ann. of Math, (to appear).
  • [R4] M. Ratner, Horocycle flows: joinings and rigidity of products, Ann. of Math. (2) 118 (1983), 277-313.
  • [W] D. Witte, Rigidity of some translations on homogeneous spaces, Invent. Math. 81 (1985), 1-27.