Baladi V.
Infinite kneading matrices and weighted zeta functions of interval maps
(52K, AMS TeX)
ABSTRACT. We consider a piecewise continuous, piecewise monotone interval map and
a weight of bounded variation, constant on homtervals and continuous at
periodic points of the map. With these data we associate
a sequence of weighted Milnor-Thurston kneading matrices, converging to a
countable matrix with coefficients analytic functions. We
show that the determinant of this infinite matrix is the inverse of the
correspondingly weighted zeta function for the map. As a corollary, we
obtain convergence of the discrete spectrum of
the Perron-Frobenius operators of piecewise linear approximations
of Markovian, piecewise expanding and piecewise $C^{1+BV}$ interval maps.
(This is a revised version of the paper sent in December 1993.)