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On the critical dimensions of product odometers

Published online by Cambridge University Press:  01 April 2009

ANTHONY H. DOOLEY  and
GENEVIEVE MORTISS
ANTHONY H. DOOLEY
Affiliation:
School of Mathematics, University of New South Wales, Sydney, NSW 2052, Australia (email: a.dooley@unsw.edu.au)
GENEVIEVE MORTISS
Affiliation:
School of Mathematics, University of New South Wales, Sydney, NSW 2052, Australia (email: a.dooley@unsw.edu.au)
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Abstract

Mortiss introduced the notion of critical dimension of a non-singular action, a measure of the order of growth of sums of Radon derivatives. The critical dimension was shown to be an invariant of metric isomorphism; this invariant was calculated for two-point product odometers and shown to coincide, in certain cases, with the average coordinate entropy. In this paper we extend the theory to apply to all product odometers, introduce upper and lower critical dimensions, and prove a Katok-type covering lemma.

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Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 29 , Issue 2 , April 2009 , pp. 475 - 485
Copyright
Copyright © Cambridge University Press 2009

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