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Perturbations of multidimensional shifts of finite type

Published online by Cambridge University Press:  22 April 2010

RONNIE PAVLOV
RONNIE PAVLOV*
Affiliation:
Department of Mathematics, The Ohio State University, Columbus, OH 43210, USA Department of Mathematics, University of British Columbia, Vancouver, BC, Canada V6T 2G3 (email: rpavlov@math.ubc.ca)
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Abstract

In this paper, we study perturbations of multidimensional shifts of finite type. Specifically, for any ℤd shift of finite type X with d>1 and any finite pattern w in the language of X, we denote by Xw the set of elements of X not containing w. For strongly irreducible X and patterns w with shape a d-dimensional cube, we obtain upper and lower bounds on htop (X)−htop (Xw) dependent on the size of w. This extends a result of Lind for d=1 . We also apply our methods to an undecidability question in ℤd symbolic dynamics.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 31 , Issue 2 , April 2011 , pp. 483 - 526
Copyright
Copyright © Cambridge University Press 2010

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