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The entropies and periods of renewal systems

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Abstract

In this work the set of entropies of shifts of finite type is proved to be the same as the set of entropies of renewal systems that are shifts of finite type. The period of a finite set of words is the greatest common divisor of the lengths of the words. We show that the period of a renewal system as a shift space and the minimum of the periods of its generating sets coincide when the system is of finite type or mixing.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon, 305-701, Korea

    Soonjo Hong & Sujin Shin

Authors
  1. Soonjo Hong
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  2. Sujin Shin
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Correspondence to Soonjo Hong.

Additional information

This work was supported by grant No.R04-2004-000-10157-0 from the Basic Research Program of the Korea Research Foundation.

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Hong, S., Shin, S. The entropies and periods of renewal systems. Isr. J. Math. 172, 9–27 (2009). https://doi.org/10.1007/s11856-009-0060-7

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  • DOI: https://doi.org/10.1007/s11856-009-0060-7

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