INFINITE KNEADING MATRICES AND WEIGHTED ZETA-FUNCTIONS OF INTERVAL MAPS

We consider a piecewise continuous, piecewise monotone interval map an d a weight of bounded variation, constant on homtervals and continuous at periodic points of the map. With these data we associate a sequenc e of weighted Milnor-Thurston kneading matrices, converging to a count able matrix with coefficients analytic functions. We show that the det erminants of these matrices converge to the inverse of the correspondi ngly weighted zeta function for the map. As a corollary, we obtain con vergence of the discrete spectrum of the Perron-Frobenius operators of piecewise linear approximations of Markovian, piecewise expanding, an d piecewise C-1+BV interval maps. (C) 1995 Academic Press, Inc.