Dynamical zeta functions for tree maps

Abstract

We study piecewise monotone and piecewise continuous maps f from a rooted oriented tree to itself, with weight functions either piecewise constant or of bounded variation. We define kneading coordinates for such tree maps. We show that the Milnor-Thurston relation holds between the weighted reduced zeta function and the weighted kneading determinant of f. This generalizes a result known for piecewise monotone interval maps.