Infinite Kneading Matrices and Weighted Zeta Functions of Interval Maps
✍ Scribed by V. Baladi
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 729 KB
- Volume
- 128
- Category
- Article
- ISSN
- 0022-1236
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✦ Synopsis
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 MilnorThurston kneading matrices, converging to a countable matrix with coefficients 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+B r}) interval maps. 1995 Academic Press. Inc.