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Approximate transitivity for zero-entropy systems

Published online by Cambridge University Press:  16 December 2004

ANTHONY DOOLEY  and
ANTHONY QUAS
ANTHONY DOOLEY
Affiliation:
School of Mathematics, University of New South Wales, Sydney, NSW 2052, Australia (e-mail: a.dooley@unsw.edu.au)
ANTHONY QUAS
Affiliation:
Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA (e-mail: aquas@memphis.edu)
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Abstract

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We show that the Morse system is approximately transitive (AT) and that a system of positive entropy cannot be AT. We give examples of zero-entropy systems that are not AT, one of which is a two-point extension of a system that is AT.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 25 , Issue 2 , April 2005 , pp. 443 - 453
Copyright
2004 Cambridge University Press