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The zeta functions of renewal systems

Published online by Cambridge University Press:  26 March 2010

SOONJO HONG
SOONJO HONG*
Affiliation:
Department of Mathematical Sciences, Seoul National University, Seoul 151-747, Korea (email: [email protected])
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Abstract

A renewal system is a shift space consisting of all bi-infinite free concatenations of some finitely many words. It is known that the zeta function of a renewal system generated by a circular set coincides with the generating function of the circular set. We extend this result to the systems generated by almost circular sets. Also we establish the formulas for the zeta functions of the systems generated by codes and pure codes, respectively. Using the formulas, we show that pure codes generating shifts of finite type are circular.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 31 , Issue 3 , June 2011 , pp. 875 - 890
Copyright
Copyright © Cambridge University Press 2010

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