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Mixing properties of numeration systems coming from weighted substitutions

Published online by Cambridge University Press:  17 July 2009

TETURO KAMAE
TETURO KAMAE*
Affiliation:
Matsuyama University, Matsuyama, 790-8578, Japan (email: [email protected])
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Abstract

A weighted substitution is a substitution that has weights associated with each occurrence of the substituted symbols. It defines a tiling space that admits the translation and scaling operators; the translation is the additive ℝ-action and the scaling is the multiplicative G-action, where G is a closed multiplicative subgroup of ℝ+. We obtained necessary and sufficient conditions for the additive action to be strongly mixing and for it to be weakly mixing.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 30 , Issue 4 , August 2010 , pp. 1111 - 1118
Copyright
Copyright © Cambridge University Press 2009

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References

[1]Kamae, T.. Numeration systems as dynamical systems. Report available at http://www14.plala.or.jp/kamae (new version of reference [2]).Google Scholar
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