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 | |
| Publication status | Published - 2017 Jan 1 |
| Externally published | Yes |
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Keywords
- Artin–Mazur zeta functions
- Negative β-transformations
- Perron–Frobenius operators
- β-transformations
ASJC Scopus subject areas
- Mathematics(all)
Cite this
Artin–mazur zeta functions of generalized beta-transformations. / Suzuki, Shintaro.
In: Kyushu Journal of Mathematics, Vol. 71, No. 1, 01.01.2017, p. 85-103.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Artin–mazur zeta functions of generalized beta-transformations
AU - Suzuki, Shintaro
PY - 2017/1/1
Y1 - 2017/1/1
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
VL - 71
SP - 85
EP - 103
JO - Kyushu Journal of Mathematics
JF - Kyushu Journal of Mathematics
SN - 1340-6116
IS - 1
ER -