Pattern generation problems arising in multiplicative integer systems

Jung Chao Ban, Wen Guei Hu, Song-Sun Lin

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageEnglish
Pages (from-to)1234-1260
Number of pages27
JournalErgodic Theory and Dynamical Systems
Issue number5
StatePublished - 1 May 2019

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