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A rank-one, rigid, simple, prime map

Published online by Cambridge University Press:  19 September 2008

A. del Junco  and
D. J. Rudolph
A. del Junco
Affiliation:
Department of Mathematics, University of Toronto, Canada, M5S 1A1
D. J. Rudolph
Affiliation:
Department of Mathematics, University of Maryland, College Park, Maryland, MA 20742, USA
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Abstract

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We construct a rank-1 map T similar to Chacon's map [C], [JRS], but with 2n+1n-blocks in an (n + 1)-block and a single spacer in the middle. Hence T is rigid and the centralizer of T, C(T), is uncountable. We show T is simple [V], [JR], and hence any factor of T is the algebra of invariant sets of some weakly compact subgroup of C(T). We show C(T) has no such subgroups and hence T is prime. Lastly we show that T is graphic in the sense of [AM].

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 7 , Issue 2 , June 1987 , pp. 229 - 247
Copyright
Copyright © Cambridge University Press 1987

References

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