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.
ASJC Scopus subject areas
- 数学 (全般)