Dynamical Zeta Functions for Maps of the Interval

Abstract

A dynamical zeta function $\zeta$ and a transfer operator $\mathcal {L}$ are associated with a piecewise monotone map $f$ of the interval [0, 1] and a weight function $g$. The analytic properties of $\zeta$ and the spectral properties of $\mathcal {L}$ are related by a theorem of Baladi and Keller under an assumption of "generating partition". It is shown here how to remove this assumption and, in particular, extend the theorem of Baladi and Keller to the case when $f$ has negative Schwarzian derivative.