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The structure of automorphisms of real suspension flows

Published online by Cambridge University Press:  19 September 2008

Harvey B. Keynes ,
Nelson G. Markley  and
Michael Sears
Harvey B. Keynes
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, Minnesota, USA
Nelson G. Markley
Affiliation:
Mathematics Department, University of Maryland, College Park, Maryland, USA
Michael Sears
Affiliation:
Department of Computational and Applied Mathematics, University of Witwatersrand, Johannesburg, RSA
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Abstract

This paper is motivated by the connections between automorphisms of real suspension flows and ℝ2 suspension actions. Automorphisms which naturally lead to ℤ2-cocyles are examined from the viewpoint of covering theory in terms of an associated cylinder flow. A natural type of automorphisms (called simple) is analyzed via ergodic methods. It is shown that all automorphisms of suspensions built over minimal rotations on tori satisfy this condition. A more general approach using eigenfunctions extends this result to minimal affines, Furstenberg-type distal flows, certain nilmanifolds and a class of non-distal flows on the 2-torus.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 11 , Issue 2 , June 1991 , pp. 349 - 364
Copyright
Copyright © Cambridge University Press 1991

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References

REFERENCES

[1]Rigge, D. De & Markley, N.. The structure of codimension one distal flows with non-trivial isotropy. Rocky Mountain J. Math. 9 (1979), 601–616.Google Scholar
[2]Furstenberg, H.. Strict ergodicity and transformations of the torus. Amer. J. Math. 83 (1961), 573–601.CrossRefGoogle Scholar
[3]Glasner, S. & Weiss, B.. On the construction of minimal skew products. Isreal J. Math. 34 4 (1979), 321–336.CrossRefGoogle Scholar
[4]Gottschalk, W. & Hedlund, G.. Topological dynamics. Amer. Math. Soc. Coll. 36 Providence, R.I. (1955).Google Scholar
[5]Hahn, F. & Parry, W.. Minimal dynamical systems with quasi-discrete spectrum. J. London Math. Soc. 40 (1965), 309–323.CrossRefGoogle Scholar
[6]Hoare, H. & Parry, W.. Affine transformations with quasi-discrete spectrum (I). J. London Math. Soc. 41 (1966), 88–96.CrossRefGoogle Scholar
[7]Keynes, H., Markley, N. & Sears, M.. Automorphisms of suspension flows over the circle. Lecture Notes in Mathematics 1342, Springer-Verlag 342–353.Google Scholar
[8]Rees, M.. A point distal transformation of the torus. Israel J. Math. 32 (1979), 201–208.CrossRefGoogle Scholar
[9]Rudolph, D.. Markov tilings of ℝn and representations of ℝn actions. In: Measure and Measurable Dynamics. Contemporary Math. 94 Amer. Math. Soc., Providence 1989, pp. 271–290.CrossRefGoogle Scholar