Duke Mathematical Journal

Limit distributions of polynomial trajectories on homogeneous spaces

Nimish A. Shah

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Article information

Duke Math. J. Volume 75, Number 3 (1994), 711-732.

First available in Project Euclid: 20 February 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 22E40: Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx]
Secondary: 22D40: Ergodic theory on groups [See also 28Dxx] 58F11


Shah, Nimish A. Limit distributions of polynomial trajectories on homogeneous spaces. Duke Math. J. 75 (1994), no. 3, 711--732. doi:10.1215/S0012-7094-94-07521-2. https://projecteuclid.org/euclid.dmj/1077287814

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  • [CFS] I. P. Cornfeld, S. V. Fomin, and Ya. G. Sinai, Ergodic theory, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 245, Springer-Verlag, New York, 1982.
  • [D1] S. G. Dani, Invariant measures of horospherical flows on noncompact homogeneous spaces, Invent. Math. 47 (1978), no. 2, 101–138.
  • [D2] S. G. Dani, A simple proof of Borel's density theorem, Math. Z. 174 (1980), no. 1, 81–94.
  • [DM1] S. G. Dani and G. A. Margulis, Values of quadratic forms at primitive integral points, Invent. Math. 98 (1989), no. 2, 405–424.
  • [DM2] S. G. Dani and G. A. Margulis, Orbit closures of generic unipotent flows on homogeneous spaces of $\rm SL(3,\bf R)$, Math. Ann. 286 (1990), no. 1-3, 101–128.
  • [DM3] S. G. Dani and G. A. Margulis, Limit distributions of orbits of unipotent flows and values of quadratic forms, I. M. Gelfand Seminar, Adv. Soviet Math., vol. 16, Amer. Math. Soc., Providence, RI, 1993, pp. 91–137.
  • [DS] S. G. Dani and J. Smillie, Uniform distribution of horocycle orbits for Fuchsian groups, Duke Math. J. 51 (1984), no. 1, 185–194.
  • [MS] S. Mozes and N. A. Shah, On the space of ergodic invariant measures of unipotent flows, to appear in Ergodic Theory Dynamical Systems.
  • [R1] M. Ratner, Strict measure rigidity for unipotent subgroups of solvable groups, Invent. Math. 101 (1990), no. 2, 449–482.
  • [R2] M. Ratner, On measure rigidity of unipotent subgroups of semisimple groups, Acta Math. 165 (1990), no. 3-4, 229–309.
  • [R3] M. Ratner, On Raghunathan's measure conjecture, Ann. of Math. (2) 134 (1991), no. 3, 545–607.
  • [R4] M. Ratner, Raghunathan's topological conjecture and distributions of unipotent flows, Duke Math. J. 63 (1991), no. 1, 235–280.
  • [R5] M. Ratner, Invariant measures and orbit closures for unipotent actions on homogeneous spaces, Geom. Funct. Anal. 4 (1994), no. 2, 236–257.
  • [S] N. A. Shah, Uniformly distributed orbits of certain flows on homogeneous spaces, Math. Ann. 289 (1991), no. 2, 315–334.