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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

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