Multidimensional sofic shifts without separation and their factors
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- by Mike Boyle, Ronnie Pavlov and Michael Schraudner PDF
- Trans. Amer. Math. Soc. 362 (2010), 4617-4653 Request permission
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.References
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Additional Information
- Mike Boyle
- Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742-4015
- MR Author ID: 207061
- ORCID: 0000-0003-0050-0542
- Email: mmb@math.umd.edu
- Ronnie Pavlov
- Affiliation: Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, British Columbia, Canada V6T 1Z2
- MR Author ID: 845553
- 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
- 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. - © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 362 (2010), 4617-4653
- MSC (2010): Primary 37B50; Secondary 37B10, 37A35, 37A15
- DOI: https://doi.org/10.1090/S0002-9947-10-05003-8
- MathSciNet review: 2645044