TY - JOUR
T1 - Artin–mazur zeta functions of generalized beta-transformations
AU - Suzuki, Shintaro
N1 - Publisher Copyright:
© 2017 Faculty of Mathematics, Kyushu University.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
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
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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 -