Artin–mazur zeta functions of generalized beta-transformations

Shintaro Suzuki

doi:10.2206/kyushujm.71.85

Artin–mazur zeta functions of generalized beta-transformations

Shintaro Suzuki

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

1 Citation (Scopus)

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)

Access to Document

10.2206/kyushujm.71.85

Cite this

@article{d1602cd1e6be443583aab685af5866fb,

title = "Artin–mazur zeta functions of generalized beta-transformations",

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",

author = "Shintaro Suzuki",

note = "Publisher Copyright: {\textcopyright} 2017 Faculty of Mathematics, Kyushu University.",

year = "2017",

doi = "10.2206/kyushujm.71.85",

language = "English",

volume = "71",

pages = "85--103",

journal = "Kyushu Journal of Mathematics",

issn = "1340-6116",

publisher = "Kyushu University, Faculty of Science",

number = "1",

}

TY - JOUR

T1 - Artin–mazur zeta functions of generalized beta-transformations

AU - Suzuki, Shintaro

PY - 2017

Y1 - 2017

N2 - 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.

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.

KW - Artin–Mazur zeta functions

KW - Negative β-transformations

KW - Perron–Frobenius operators

KW - β-transformations

UR - http://www.scopus.com/inward/record.url?scp=85019898929&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85019898929&partnerID=8YFLogxK

U2 - 10.2206/kyushujm.71.85

DO - 10.2206/kyushujm.71.85

M3 - Article

AN - SCOPUS:85019898929

VL - 71

SP - 85

EP - 103

JO - Kyushu Journal of Mathematics

JF - Kyushu Journal of Mathematics

SN - 1340-6116

IS - 1

ER -

Artin–mazur zeta functions of generalized beta-transformations

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this