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Pattern generation problems arising in multiplicative integer systems

Published online by Cambridge University Press:  25 September 2017

JUNG-CHAO BAN ,
WEN-GUEI HU  and
SONG-SUN LIN
JUNG-CHAO BAN
Affiliation:
Department of Applied Mathematics, National Dong Hwa University, Hualien 97401, Taiwan email [email protected]
WEN-GUEI HU
Affiliation:
College of Mathematics, Sichuan University, Chengdu, 610064, China email [email protected]
SONG-SUN LIN
Affiliation:
Department of Applied Mathematics, National Chiao Tung University, Hsin-Chu 30010, Taiwan email [email protected]
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Abstract

This study investigates a multiplicative integer system, an invariant subset of the full shift under the action of the semigroup of multiplicative integers, by using a method that was developed for studying pattern generation problems. The spatial entropy and the Minkowski dimensions of general multiplicative systems can thus be computed. A coupled system is the intersection of a multiplicative integer system and the golden mean shift, which can be decoupled by removing the multiplicative relation set and then performing procedures similar to those applied to a decoupled system. The spatial entropy can be obtained after the remaining error term is shown to approach zero.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 39 , Issue 5 , May 2019 , pp. 1234 - 1260
Copyright
© Cambridge University Press, 2017 

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