A weakly mixing upside-down tower of isometric extensions

S. Glasner; B. Weiss

doi:10.1017/S0143385700009196

A weakly mixing upside-down tower of isometric extensions

S. Glasner
, B. Weiss^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

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 Π_{n, m}, for n<m, be the projection of Xnon X_m, S induces for every n, a homeomorphism of Xnand the extensions are isometric. We also show that, for every S in this family, (S, X) is disjoint from every purely weakly mixing flow.

Original language	English
Pages (from-to)	151-157
Number of pages	7
Journal	Ergodic Theory and Dynamical Systems
Volume	1
Issue number	2
DOIs	https://doi.org/10.1017/S0143385700009196
State	Published - Jun 1981
Externally published	Yes

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AB - 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 nm, S induces for every n, a homeomorphism of Xnand the extensions are isometric. We also show that, for every S in this family, (S, X) is disjoint from every purely weakly mixing flow.

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A weakly mixing upside-down tower of isometric extensions

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