Journal
ERGODIC THEORY AND DYNAMICAL SYSTEMS
Volume 30, Issue -, Pages 489-523Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/S0143385709000194
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Funding
- NSF [DMS-0300398, DMS-0600956]
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We consider a subclass of tilings: the tilings obtained by cut-and-projection. Under somewhat standard assumptions, we show that the natural complexity function has polynomial growth. We compute its exponent a in terms of the ranks of certain groups which appear in the construction. We give bounds for a. These computations apply to some well-known tilings, such as the octagonal tilings, or tilings associated with billiard sequences. A link is made between the exponent of the complexity, and the fact that the cohomoloay of the associated tiling space is finitely generated over Q. We show that such a link cannot be established for more general filings, and we present a counterexample in dimension one.
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