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Distal and proximal extensions of minimal flows

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References

  1. J. Auslander, Endomorphisms of minimal sets,Duke Math. J. 30 (1963), 605–614.

    Google Scholar 

  2. J. Auslander, Regular minimal sets. I,Trans. Amer. Math. Soc. 123 (1966), 469–479.

    Google Scholar 

  3. J. Auslander andB. Horelick, Regular minimal sets. II: The proximally equicontinuous case (to appear).

  4. R. Ellis, A semigroup associated with a transformation group,Trans. Amer. Math Soc. 94 (1960), 272–281.

    Google Scholar 

  5. R. Ellis, Construction of minimal discrete flows,Amer. J. Math. 87 (1965), 564–574.

    Google Scholar 

  6. R. Ellis, Group-like extensions of minimal sets,Trans. Amer. Math. Soc. 127 (1967), 125–135.

    Google Scholar 

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

    Google Scholar 

  8. H. Furstenberg, Structure of distal flows,Amer. J. Math. 85 (1963), 477–515.

    Google Scholar 

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

    Google Scholar 

  10. W. Gottschalk andR. Ellis, Homomorphisms of transformation groups,Trans. Amer. Math. Soc. 127 (1967), 125–135.

    Google Scholar 

  11. W. Gottschalk andG. Hedlund, Topological Dynamics,Amer. Math. Soc. Colloq. Publ., Vol. 36, Providence, 1955.

  12. G. Hedlund, Sturmian minimal sets,Amer. J. Math. 66 (1944), 605–620.

    Google Scholar 

  13. N. Jacobson,Lectures in Abstract Algebra, Vol. III, Van Nostrand, Princeton, 1964.

    Google Scholar 

  14. J. L. Kelley,General Topology, Van Nostrand, Princeton, 1955.

    Google Scholar 

  15. H. Keynes andJ. Robertson, Eigenvalue theorems in topological transformation groups,Trans. Amer. Math. Soc. 139 (1969), 359–369.

    Google Scholar 

  16. A. Knapp, Functions behaving like almost automorphic functions,Topological Dynamics an International Symposium, edited by J. Auslander and W. Gottschalk, Benjamin, New York, 1968, pp. 299–317.

    Google Scholar 

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

    Google Scholar 

  18. L. Shapiro, Distal and proximal extensions of minimal flows, Ph.D. Thesis, Yale University, 1962.

  19. L. Shapiro, The structure of H-cascades, (to appear).

  20. W. Veech, The equicontinuous structure relation for minimal abelian transformation groups,Amer. J. Math. 90 (1968), 723–732.

    Google Scholar 

  21. W. Veech, Point-distal flows,Amer. J. Math. 92 (1970) 205–242.

    Google Scholar 

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Authors and Affiliations

  1. University of Minnesota, USA

    Leonard Shapiro

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  1. Leonard Shapiro
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Supported by an NSF Graduate Fellowship at Yale University and by NSF grant GP-8691.

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Shapiro, L. Distal and proximal extensions of minimal flows. Math. Systems Theory 5, 76–88 (1971). https://doi.org/10.1007/BF01691470

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