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On the ergodicity of frame flows. (English) Zbl 0445.58023


MSC:

37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
53D25 Geodesic flows in symplectic geometry and contact geometry
37C10 Dynamics induced by flows and semiflows
37A99 Ergodic theory
53C20 Global Riemannian geometry, including pinching
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References:

[1] Anosov, D.V.: Geodesic flows on closed Riemannian manifolds of negative curvature. Proc. Steklov Inst. Math.90 (1967) · Zbl 0176.19101
[2] Borel, A.: Compact Clifford-Klein forms of symmetric spaces. Topology.2, 111-122 (1963) · Zbl 0116.38603
[3] Borel, A., Serre, J.-P.: Groupes de Lie et puissances réduites de Steenrod. Amer. J. Math.75, 409-448 (1953) · Zbl 0050.39603
[4] Bott, R.: Lectures onK(X). New York, Amsterdam; W.A. Benjamin, Inc. 1969 · Zbl 0194.23904
[5] Brin, M.: Topology transitivity of one class of dynamical systems and flows of frames on manifolds of negative curvature. Funct. Analysis and Its Applic.9, 8-16 (1975) · Zbl 0357.58011
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[8] Gromov, M.: On a geometric Banach’s problem. Izvestija AN SSSR, ser. mat.31, 1105-1114 (1967) (in Russian)
[9] Hu, S.T.: Homotopy Theory. New York, London: Academic Press 1959 · Zbl 0088.38803
[10] Mimura, M.: The homotopy groups of Lie groups of low rank. J. Math. Kyoto Univ.6, 131-176 (1967) · Zbl 0171.44101
[11] Mimura, M., Toda, H.: Homotopy groups of symplectic groups. J. Math. Kyoto Univ.3, 251-273 (1964). · Zbl 0129.15405
[12] Onisçik, A.L.: On Lie groups transitive on compact manifolds III. Mathematics of the USSR-Sbornik4, 233-240 (1968) · Zbl 0198.29001
[13] Ratner, M.: Anosov flows with Gibbs measures are also Bernoullian. Israel J. Math.17, 380-391 (1974) · Zbl 0304.28011
[14] Rudolph, D.J.: Classifying the isometric extensions, of a Bernoulli shift. J. d’Analyse Mathematique34, 36-60 (1978) · Zbl 0415.28012
[15] Steenrod, N.: The Topology of Fibre Bundles. Princeton New Jersey: Princeton Univ. Press 1951 · Zbl 0054.07103
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