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Transactions of the American Mathematical Society
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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1973-0322839-1
PII: S 0002-9947(1973)0322839-1
Keywords: Induced transformations, minimal sets, weak mixing, strong mixing, symbolic dynamics, Toeplitz sequences, Sturmian sequences, uniform distribution $ \bmod\;1$
Article copyright: © Copyright 1973 American Mathematical Society