Dynamical Zeta functions for differentiable parabolic maps of the interval

Abstract

This paper explores the domain of meromorphic extension for the dynamical zeta function associated to a class of one-dimensional differentiable parabolic maps featuring an indifferent fixed point. We establish the connection between this domain and the spectrum of the weighted transfer operators of the induced map. Furthermore, we discuss scenarios where meromorphic extensions occur beyond the confines of the natural disc of convergence of the dynamical zeta function.