Dani, S. G. Invariant measures and minimal sets of horospherical flows. (English) Zbl 0498.58013 Invent. Math. 64, 357-385 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 6 ReviewsCited in 38 Documents MSC: 37A99 Ergodic theory 37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) 53D25 Geodesic flows in symplectic geometry and contact geometry 22D40 Ergodic theory on groups 28D10 One-parameter continuous families of measure-preserving transformations 22E40 Discrete subgroups of Lie groups 22E46 Semisimple Lie groups and their representations Keywords:ergodicity of horocycle flows; reductive Lie group; maximal horospherical subgroup; unique ergodicity of flows; arithmetic lattices PDFBibTeX XMLCite \textit{S. G. Dani}, Invent. Math. 64, 357--385 (1981; Zbl 0498.58013) Full Text: DOI EuDML References: [1] Borel, A.: Introduction aux groupes arithmetiques, Publ. de l’Inst. Math. de l’Univ. de Strasbourg XV. Paris: Hermann 1969 [2] Borel, A., Harish-Chandra: Arithmetic subgroups of algebraic groups, Ann. of Math.75, 485-535 (1962) · Zbl 0107.14804 [3] Borel, A., Tits, J.: Groupes reductifs, Inst. Hautes Etudes Sci. Publ. Math.27, 55-150 (1965) · Zbl 0145.17402 [4] Borel, A., Tits, J.: Complements A l’article ?Groupes reductifs?, Inst. Hautes Etudes Sci. Publ. Math.41, 253-276 (1972) · Zbl 0254.14018 [5] Browen, R.: Weak mixing and unique ergodicity on homogeneous spaces, Israel J. Math.23, 267-273 (1976) · Zbl 0338.43014 [6] Dani, J.S.: Density properties of orbits under discrete groups, J. Indian Math. Soc.39, 189-218 (1975) · Zbl 0428.22006 [7] Dani, S.G.: Spectrum of an affine transformation, Duke Math. J.44, 129-155 (1977) · Zbl 0351.22005 [8] Dani, S.G.: Invariant measures of horospherical flows on non-compact homogeneous spaces, Invent math.47, 101-138 (1978) · Zbl 0384.28015 [9] Dani, S.G.: On invariant measures, minimal sets and a lemma of Margulis, Invent math.51, 239-260 (1979) · Zbl 0415.28008 [10] Dani, S.G., Raghavan, S.: Orbits of euclidean frames under discrete linear groups, Israel J. Math.36, 300-320 (1980) · Zbl 0457.28008 [11] Ellis, R.: Lectures on topological dynamics, New York: W.A. Benjamin 1969 · Zbl 0193.51502 [12] Ellis, R., Perrizo, W.: Unique ergodicity of flows on homogeneous spaces, Israel J. Math.29, 276-284 (1978) · Zbl 0383.22004 [13] Furstenberg, H.: Strict ergodicity and transformations of the torus, Amer. J. Math.83, 573-601 (1961) · Zbl 0178.38404 [14] Furstenberg, H.: The unique ergodicity of the horocycle flow, Recent Advances in Topological Dynamics (A. Beck. ed.) pp. 95-115, Berlin, Heidelberg, New York: Springer 1972 [15] Garland, H., Raghunathan, M.S.: Fundamental domains for lattices in ø-rank 1 semisimple Lie groups, Ann. of Math.92, 279-326 (1970) · Zbl 0206.03603 [16] Humphreys, J.E.: Introduction to Lie algebras and representation theory, Berlin-Heidelberg-New York: Springer 1972 · Zbl 0254.17004 [17] Humphreys, J.E.: Linear algebraic groups, Berlin-Heidelberg-New York: Springer 1975 · Zbl 0325.20039 [18] Margulis, G.A.: Arithmetic properties of discrete subgroups, Uspehi Mat. Nauk 29:1, 49-98 (1974)=Russian Math. Surveys 28:1, 107-156 (1974) · Zbl 0299.22010 [19] Moore, C.C.: Ergodicity of flows on homogeneous spaces, Amer. J. Math.88, 154-178 (1966) · Zbl 0148.37902 [20] Parry, W.: Ergodic properties of affine transformations and flows on nilmanifolds, Amer. J. Math.91, 757-771 (1969) · Zbl 0183.51503 [21] Raghunathan, M.S.: Discrete subgroups of Lie groups, Berlin-Heidelberg-New York: Springer 1972 · Zbl 0254.22005 [22] Schmidt, K.A.: Probabilistic proof of ergodic decomposition, Sankhya: The Indian Journal of Statistics40, 10-18 (1978) [23] Varadarajan, V.S.: Groupes of automorphisms of Borel spaces, Trans. Amer. Math. Soc.109, 191-220 (1963) · Zbl 0192.14203 [24] Veech, W.A.: Unique ergodicity of horospherical flows, Amer. J. Math.99, 827-859 (1977) · Zbl 0365.28012 [25] Warner, G.: Harmonic analysis on semisimple Lie groups I, Berlin-Heidelberg-New York: Springer 1972 · Zbl 0265.22020 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.