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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Multidimensional sofic shifts without separation and their factors


Authors: Mike Boyle, Ronnie Pavlov and Michael Schraudner
Journal: Trans. Amer. Math. Soc. 362 (2010), 4617-4653
MSC (2010): Primary 37B50; Secondary 37B10, 37A35, 37A15
Published electronically: April 9, 2010
MathSciNet review: 2645044
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Abstract: For $ d\geq 2$ we exhibit mixing $ \mathbb{Z}^d$ shifts of finite type and sofic shifts with large entropy but poorly separated subsystems (in the sofic examples, the only minimal subsystem is a single point). These examples consequently have very constrained factors; in particular, no non-trivial full shift is a factor. We also provide examples to distinguish certain mixing conditions and develop the natural class of ``block gluing'' shifts. In particular, we show that block gluing shifts factor onto all full shifts of strictly smaller entropy.


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Additional Information

Mike Boyle
Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742-4015
Email: mmb@math.umd.edu

Ronnie Pavlov
Affiliation: Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, British Columbia, Canada V6T 1Z2
Email: rpavlov@math.ubc.ca

Michael Schraudner
Affiliation: Centro de Modelamiento Matematico, Universidad de Chile, Av. Blanco Encalada 2120, Piso 7, Santiago de Chile
Email: mschraudner@dim.uchile.cl

DOI: http://dx.doi.org/10.1090/S0002-9947-10-05003-8
PII: S 0002-9947(10)05003-8
Keywords: $\mathbb {Z}^d$, shift of finite type, sofic, minimal subshift, factor, subsystem, mixing, entropy, multidimensional
Received by editor(s): June 25, 2008
Published electronically: April 9, 2010
Additional Notes: The first author was partly supported by Dassault Chair, Nucleus Millennium P04-069-F, NSF Grant 0400493, and Basal-CMM grant.
The third author was supported by FONDECYT project 3080008.
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.