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arXiv:1805.02213 [math.DS]AbstractReferencesReviewsResources

Uniform Distribution of Kakutani Partitions Generated By Substitution Schemes

Yotam Smilansky

Published 2018-05-06Version 1

The main result of this paper is a proof of uniform distribution for a large family of sequences of partitions, constituting a generalization of a result of Kakutani regarding partitions of the unit interval. A sequence is defined according to a multiscale substitution scheme on a set of prototiles, which is a set of substitution rules determining a tiling of each prototile by rescaled copies of the prototiles at hand. Given a multiscale substitution scheme, a succession of substitutions of tiles is used to define a sequence of partitions, which is studied using a directed weighted graph associated with the scheme.

Comments: 24 pages, 20 figures
Categories: math.DS
Subjects: 05B45, 52C23, 11K36, 60B10, 05C21
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