On the Entropy of Multidimensional Multiplicative Integer Subshifts

Abstract

A multiplicative integer subshift \(X_\Omega \) derived from the subshift \(\Omega \) is invariant under multiplicative integer action, which is closely related to the level set of multiple ergodic average. The complexity of \(X_{\Omega }\) is usually measured by entropy (or box dimension). This work concerns on two types of multi-dimensional multiplicative integer subshifts (MMIS) with different coupling constraints, and then obtains their entropy formulae.

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Acknowledgements

The authors wish to express their gratitude to the editor and the anonymous referees for their careful reading and useful suggestions, which make significant improvements of this work.

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Correspondence to Wen-Guei Hu.

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Ban is partially supported by the Ministry of Science and Technology, ROC (Contract MOST 107-2115-M-259 -001 -MY2 and 107-2115-M-390 -002 -MY2). Hu is partially supported by the National Natural Science Foundation of China (Grant 11601355)

Communicated by Alessandro Giuliani.

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Ban, JC., Hu, WG. & Lai, GY. On the Entropy of Multidimensional Multiplicative Integer Subshifts. J Stat Phys 182, 31 (2021). https://doi.org/10.1007/s10955-021-02703-7

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Keywords

  • Entropy
  • Multiplicative integer subshift
  • Multiple ergodic average
  • Box dimension