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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



A topologically strongly mixing symbolic minimal set

Author: K. E. Petersen
Journal: Trans. Amer. Math. Soc. 148 (1970), 603-612
MSC: Primary 54.82
MathSciNet review: 0259884
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Abstract: Recent papers by the author, Keynes and Robertson, and others have shown that weakly mixing minimal flows are objects of considerable interest, but examples of such flows, other than the horocycle flows, have been scarce. We give here a ``machinal'' construction of a bilateral sequence with entries from 0, 1 whose orbit closure is topologically strongly mixing and minimal. We prove in addition that the flow we obtain has entropy zero, is uniquely ergodic, and fails to be measure-theoretically strongly mixing.

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Keywords: Minimal sets, strong mixing, weak mixing, symbolic dynamics
Article copyright: © Copyright 1970 American Mathematical Society