Dynamical zeta functions for maps of the interval

Abstract

A dynamical zeta function $\zeta$ and a transfer operator $\scr L$ 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 $\scr L$ 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.