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ISSN 1088-6850(e) ISSN 0002-9947(p)

Multidimensional sofic shifts without separation and their factors

Author(s): Mike Boyle; Ronnie Pavlov; Michael Schraudner
Journal: Trans. Amer. Math. Soc. 362 (2010), 4617-4653.
MSC (2010): Primary 37B50; Secondary 37B10, 37A35, 37A15
Posted: April 9, 2010
MathSciNet review: 2645044
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

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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