ARTIN-MAZUR ZETA FUNCTIONS OF GENERALIZED BETA-TRANSFORMATIONS
キーワード:
β-transformations,
negative β-transformations,
Artin-Mazur zeta functions,
Perron-Frobenius operators
2017 年 71 巻 1 号 p. 85-103
詳細
2017 年 71 巻 1 号 p. 85-103
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.
