A topologically strongly mixing symbolic minimal set

Petersen, K. E.

doi:10.1090/S0002-9947-1970-0259884-8

A topologically strongly mixing symbolic minimal set
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Trans. Amer. Math. Soc. 148 (1970), 603-612 Request permission

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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