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Transactions of the American Mathematical Society

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



Induced flows

Authors: Karl Petersen and Leonard Shapiro
Journal: Trans. Amer. Math. Soc. 177 (1973), 375-390
MSC: Primary 54H20; Secondary 10K30
MathSciNet review: 0322839
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Abstract: The construction of induced transformations is considered in the setting of topological dynamics. Sufficient conditions are given for induced flows to be topologically weakly mixing, and it is proved that Toeplitz flows and certain Sturmian flows satisfy these conditions and give rise to new and easily constructed classes of flows which have entropy zero and are uniquely ergodic, minimal, and topologically weakly mixing. An example is given of a weakly mixing minimal flow which is not topologically strongly mixing.

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Keywords: Induced transformations, minimal sets, weak mixing, strong mixing, symbolic dynamics, Toeplitz sequences, Sturmian sequences, uniform distribution <IMG WIDTH="62" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$\bmod \;1$">
Article copyright: © Copyright 1973 American Mathematical Society