Transitive sofic spacing shifts

John Banks; Piotr Oprocha; Brett Stanley

doi:10.3934/dcds.2015.35.4743

Article Contents

2015, Volume 35, Issue 10: 4743-4764. Doi: 10.3934/dcds.2015.35.4743

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Transitive sofic spacing shifts

1.
Department of Mathematics and Statistics, University of Melbourne, Parkville 3010
2.
Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków
3.
Department of Mathematics and Statistics, La Trobe University, Bundoora 3086

Received: April 30, 2014

Revised: January 31, 2015

Published: September 2015

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Abstract

Spacing shifts were introduced by Lau and Zame in the 1970's to provide accessible examples of maps that are weakly mixing but not mixing. In previous papers by the authors and others, it has been observed that the problem of describing when spacing shifts are topologically transitive appears to be quite difficult in general. In the present paper, we give a characterization of sofic spacing shifts and begin to investigate which sofic spacing shifts are topologically transitive. We show that the canonical graph presentation of such a shift has a rather simple form, for which we introduce the terminology hereditary bunched cycle and discuss the apparently difficult problem of determining which hereditary bunched cycles actually present spacing shifts.

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Mathematics Subject Classification: Primary: 37B10; Secondary: 37B20, 05C38, 68Q45.

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References

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