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Extension of minimal transformation groups

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References

  1. H. Anzai, Ergodic skew transformations on the torus,Osaka Math. J. 3 (1951), 83–99.

    Google Scholar 

  2. R. Ellis, The construction of minimal discrete flows,Amer. J. Math. 87 (1965), 564–574.

    Google Scholar 

  3. R. Ellis,Lectures on Topological Dynamics, W. A. Benjamin, New York, 1969.

    Google Scholar 

  4. R. Ellis andW. H. Gottschalk, Homomorphisms of transformation groups,Trans. Amer. Math. Soc. 94 (1960), 258–271.

    Google Scholar 

  5. H. Furstenberg, Strict ergodicity and transformation of the torus,Amer. J. Math. 83 (1961), 573–601.

    Google Scholar 

  6. H. Furstenberg, The structure of distal flows,Amer. J. Math. 85 (1963), 477–515.

    Google Scholar 

  7. H. Furstenberg, Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation,Math. Systems Theory 1 (1967), 1–49.

    Google Scholar 

  8. H. B. Keynes andJ. B. Robertson, Eigenvalue theorems in topological transformation groups,Trans. Amer. Math. Soc. 139 (1969), 359–370.

    Google Scholar 

  9. S. Maclane,Homology, Springer-Verlag, Berlin, 1963.

    Google Scholar 

  10. W. Parry, Compact abelian group extensions of discrete dynamical systems,Z. Wahrscheinlichkeitstheorie Verw. Geb. 13 (1969), 95–113.

    Google Scholar 

  11. R. Peleg, Some extensions of weakly mixing flows, Dissertation, Hebrew University, 1970.

  12. K. E. Petersen, Disjointness and weak mixing of minimal sets,Proc. Amer. Math. Soc. 24 (1970), 278–280.

    Google Scholar 

  13. K. E. Petersen, A topologically strongly mixing symbolic minimal set,Trans. Amer. Math. Soc. 148 (1970), 603–612.

    Google Scholar 

  14. L. Shapiro, Distal and proximal extensions of minimal flows,Math. Systems Theory 5 (1971), 76–88.

    Google Scholar 

  15. W. A. Veech, Strict ergodicity in zero-dimensional dynamical systems and the Kronecker-Weyl theorem mod 2,Trans. Amer. Math. Soc. 140 (1969), 1–34.

    Google Scholar 

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Supported in part by NSF grant GP-19758.

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Petersen, K.E. Extension of minimal transformation groups. Math. Systems Theory 5, 365–375 (1971). https://doi.org/10.1007/BF01694081

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  • DOI: https://doi.org/10.1007/BF01694081

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