Artin–mazur zeta functions of generalized beta-transformations

Shintaro Suzuki

doi:10.2206/kyushujm.71.85

Artin–mazur zeta functions of generalized beta-transformations

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	85-103
Number of pages	19
Journal	Kyushu Journal of Mathematics
Volume	71
Issue number	1
DOIs	https://doi.org/10.2206/kyushujm.71.85
Publication status	Published - 2017
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Mathematics(all)

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10.2206/kyushujm.71.85

Cite this

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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 G{\'o}ra [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.",

keywords = "Artin–Mazur zeta functions, Negative β-transformations, Perron–Frobenius operators, β-transformations",

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AB - 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.

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Artin–mazur zeta functions of generalized beta-transformations

Abstract

Keywords

ASJC Scopus subject areas

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