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A weakly mixing upside-down tower of isometric extensions

Published online by Cambridge University Press:  19 September 2008

S. Glasner  and
B. Weiss
S. Glasner
Affiliation:
Tel Aviv University and the Hebrew University of Jerusalem
B. Weiss*
Affiliation:
Tel Aviv University and the Hebrew University of Jerusalem
*
†Address for correspondence: Dr B. Weiss, Department of Mathematics, Hebrew University of Jerusalem, Jerusalem, Israel.
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Abstract

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On the infinite torus X = , using a category argument, we produce a large family of homeomorphisms such that for every element S in this family the flow (S, X) is weakly mixing and strictly ergodic. Moreover, writing Xn = {n, n + 1…} and letting Πn, m, for n<m, be the projection of Xn on Xm, S induces for every n, a homeomorphism of Xn and the extensions are isometric. We also show that, for every S in this family, (S, X) is disjoint from every purely weakly mixing flow.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 1 , Issue 2 , June 1981 , pp. 151 - 157
Copyright
Copyright © Cambridge University Press 1981

References

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