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Weak mixing and unique ergodicity on homogeneous spaces

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Abstract

Under certain conditions the weak mixing of a translation onG/Γ implies that the action of an associated subgroup ofG onG/Γ is uniquely ergodic. This result generalizes earlier theorems of Furstenberg and Veech.

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References

  1. D. Anosov,Geodesic flows on closed Riemann manifolds with negative curvature, Proc. Steklov Inst. Math.90 (1967).

  2. R. Bowen and B. Marcus,Unique ergodicity of horocycle foliations, to appear.

  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.

  6. B. Marcus,Unique ergodicity of the horocycle flow: variable negative curvature case, Israel J. Math.21 (1975), 133–144.

    Article  MathSciNet  MATH  Google Scholar 

  7. C. Moore,Ergodicity of flows on homogeneous spaces, Amer. J. Math.88 (1966), 154–178.

    Article  MathSciNet  MATH  Google Scholar 

  8. C. Pugh and M. Shub,Ergodic elements of ergodic actions, Compositio Math.23 (1971), 115–122.

    MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  11. W. Veech,Unique ergodicity of horospherical flows, Israel J. Math.21 (1975), 233–239.

    Article  MathSciNet  MATH  Google Scholar 

  12. F. Mautner,Geodesic flows on symmetric Riemann spaces, Ann. of Math.65 (1957), 416–431.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of California, 94720, Berkeley, Calif., U.S.A.

    Rufus Bowen

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  1. Rufus Bowen
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Partially supported by the Sloan Foundation and NSF GP-14519.

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Bowen, R. Weak mixing and unique ergodicity on homogeneous spaces. Israel J. Math. 23, 267–273 (1976). https://doi.org/10.1007/BF02761804

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  • DOI: https://doi.org/10.1007/BF02761804

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