Artin–mazur zeta functions of generalized beta-transformations

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Abstract

In this paper, we study the Artin–Mazur zeta function of a generalization of the well-known β-transformation introduced by Góra [Invariant densities for generalized β-maps. Ergodic Theory Dynam. Systems 27 (2007), 1583–1598].We show that the Artin– Mazur zeta function can be extended to a meromorphic function via an expansion of 1 defined by using the transformation. As an application, we relate its analytic properties to the algebraic properties of β.

Original languageEnglish
Pages (from-to)85-103
Number of pages19
JournalKyushu Journal of Mathematics
Volume71
Issue number1
DOIs
Publication statusPublished - 2017
Externally publishedYes

Keywords

  • Artin–Mazur zeta functions
  • Negative β-transformations
  • Perron–Frobenius operators
  • β-transformations

ASJC Scopus subject areas

  • Mathematics(all)

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