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Weak mixing and unique ergodicity on homogeneous spaces. (English) Zbl 0338.43014


MSC:

43A85 Harmonic analysis on homogeneous spaces
43A05 Measures on groups and semigroups, etc.
60B15 Probability measures on groups or semigroups, Fourier transforms, factorization
28D05 Measure-preserving transformations
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References:

[1] D. Anosov,Geodesic flows on closed Riemann manifolds with negative curvature, Proc. Steklov Inst. Math.90 (1967). · Zbl 0176.19101
[2] R. Bowen and B. Marcus,Unique ergodicity of horocycle foliations, to appear. · Zbl 0346.58009
[3] H. Furstenberg,The unique ergodicity of the horocycle flow, inRecent Advances in Topological Dynamics, Springer-Verlag Lecture Notes 318, pp. 95–114.
[4] P. Halmos,Lectures on Ergodic Theory, Chelsea, 1956.
[5] S. Helgason,Differential Geometry and Symmetric Spaces, Academic Press, 1962. · Zbl 0111.18101
[6] B. Marcus,Unique ergodicity of the horocycle flow: variable negative curvature case, Israel J. Math.21 (1975), 133–144. · Zbl 0314.58013 · doi:10.1007/BF02760791
[7] C. Moore,Ergodicity of flows on homogeneous spaces, Amer. J. Math.88 (1966), 154–178. · Zbl 0148.37902 · doi:10.2307/2373052
[8] C. Pugh and M. Shub,Ergodic elements of ergodic actions, Compositio Math.23 (1971), 115–122. · Zbl 0225.28009
[9] V. Rohlin,On the Fundamental Ideas of Measure Theory, Amer. Math. Soc. No. 71.
[10] A. Stepin,Dynamical systems on homogeneous spaces of semi-simple Lie groups, Math. USSR-Izv.7 (1973), 1089–1104. · Zbl 0314.28014 · doi:10.1070/IM1973v007n05ABEH001995
[11] W. Veech,Unique ergodicity of horospherical flows, Israel J. Math.21 (1975), 233–239. · Zbl 0334.28013 · doi:10.1007/BF02760800
[12] F. Mautner,Geodesic flows on symmetric Riemann spaces, Ann. of Math.65 (1957), 416–431. · Zbl 0084.37503 · doi:10.2307/1970054
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