Skip to main content
Log in

Regular minimal sets over the circle and the ellis minimal set

  • Published:
Mathematical systems theory Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. J. Auslander, The proximal relation in topological dynamics,Proc. Amer. Math. Soc. 11 (1960), 890–895.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  4. J. Auslander andB. Horelick, Regular minimal sets II: The proximally equicontinuous case,Compositio Math., to appear.

  5. R. Ellis, Distal transformation groups,Pacific J. Math. 8 (1958), 401–405.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  9. J. L. Kelley,General Topology, D. Van Nostrand, Princeton, 1955.

    Google Scholar 

  10. H. B. Keynes, On the proximal relation being closed,Proc. Amer. Math. Soc. 18 (1967), 518–522.

    Google Scholar 

  11. N. G. Markley, Transitive homeomorphisms of the circle,Math. Systems Theory 2 (1968), 247–249.

    Google Scholar 

  12. N. G. Markley, Homeomorphisms of the circle without periodic points,J. London Math. Soc., to appear.

  13. H. Poincaré, Sur les courbes définies par les équations différentielles,J. Math. Pures Appl. (4) 1 (1885), 167–244.

    Google Scholar 

  14. E. R. van Kampen, The topological transformations of a simple closed curve onto itself,Amer. J. Math. 57 (1935), 142–152.

    Google Scholar 

  15. L. Shapiro, Distal and proximal extensions of minimal flows, Dissertation, Yale University, 1969.

  16. T. S. Wu, Construction of locally almost periodic minimal transformation groups,Math. Systems Theory 1 (1967), 157–163.

    Google Scholar 

  17. T. S. Wu, Two homomorphic but not isomorphic minimal sets,Michigan Math. J. 14 (1967), 401–404.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

The material in this paper is a portion of a Ph.D. thesis submitted to the University of Maryland. The author is grateful to Professor Nelson G. Markley for his many valuable suggestions.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Freiman, R. Regular minimal sets over the circle and the ellis minimal set. Math. Systems Theory 6, 145–163 (1972). https://doi.org/10.1007/BF01706086

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01706086

Keywords

Navigation