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Pattern generation problems arising in multiplicative integer systems

  • JUNG-CHAO BAN (a1), WEN-GUEI HU (a2) and SONG-SUN LIN (a3)

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.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
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