Infinite Kneading Matrices and Weighted Zeta Functions of Interval Maps
نویسنده
چکیده
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 coeecients analytic functions. We show that the determinants of these matrices converge to 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.
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