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[B]Bowen, R., Weak mixing and unique ergodicity on homogeneous spaces.Israel J. Math., 23 (1976), 267–273.
[BM]Brezin, J. &Moore, C., Flows on homogeneous spaces: a new look.Amer. J. Math., 103 (1981), 571–613.
[D1]Dani, S. G., Invariant measures of horospherical flows on noncompact homogeneous spaces.Invent. Math., 47 (1978), 101–138.
[D2]—, Invariant measures and minimal sets of horospherical flows.Invent. Math., 64 (1981), 357–385.
[EP]Ellis, R. &Perrizo, W., Unique ergodicity of flows on homogeneous spaces.Israel J. Math., 29 (1978), 276–284.
[F1]Furstenberg, H., Strict ergodicity and transformations of the torus.Amer. J. Math., 83 (1961), 573–601.
[F2]Furstenberg, H., The unique ergodicity of the horocycle flow, inRecent Advances in Topological Dynamics, 95–115. Springer, 1972.
[GE]Greenleaf, P. &Emerson, W. R., Group structure and pointwise ergodic theorem for connected amenable groups.Adv. in Math., 14 (1974), 153–172.
[H]Humphreys, J.,Introduction to Lie Algebras and Representation Theory. Springer-Verlag, 1972.
[J]Jacobson, N.,Lie Algebras. John Wiley, 1962.
[M]Margulis, G. A., Discrete subgroups and ergodic theory.Symposium in honor of A. Selberg, Number theory, trace formulas and discrete groups. Oslo, 1989.
[P]Parry, W., Ergodic properties of affine transformations and flows on nilmanifolds.Amer. J. Math., 91 (1969), 757–771.
[R1]Ratner, M., Rigidity of horocycle flows.Ann. of Math., 115 (1982), 597–614.
[R2] —, Factors of horocycle flows.Ergodic Theory Dynamical Systems, 2 (1982), 465–489.
[R3] —, Horocycle flows: joinings and rigidity of products.Ann. of Math., 118 (1983), 277–313.
[R4] —, Strict measure rigidity for unipotent subgroups of solvable groups.Invent. Math., 101 (1990), 449–482.
[R5] —, Invariant measures for unipotent translations on homogeneous spaces.Proc. Nat. Acad. Sci. U.S.A., 87 (1990), 4309–4311.
[Ve]Veech, W., Unique ergodicity of horospherical flows.Amer. J. Math., 99 (1977), 827–859.
[W1]Witte, D., Rigidity of some translations on homogeneous spaces.Invent. Math., 81 (1985), 1–27.
[W2] —, Zero entropy affine maps on homogeneous spaces.Amer. J. Math., 109 (1987), 927–961.
[W3]Witte, D., Measurable quotients of unipotent translations on homogeneous spaces. To appear.
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Partially supported by Guggenheim Foundation Fellowship and NSF Grant DMS-8701840.
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Ratner, M. On measure rigidity of unipotent subgroups of semisimple groups. Acta Math. 165, 229–309 (1990). https://doi.org/10.1007/BF02391906
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DOI: https://doi.org/10.1007/BF02391906