Dynamical Zeta Functions for Piecewise Monotone Maps of the Interval

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Consider a space $M$, a map $f:M\to M$, and a function $g:M \to {\mathbb C}$. The formal power series $\zeta (z) = \exp \sum ^\infty_{m=1} \frac {z^m} {m} \sum_{x \in \mathrm {Fix}\,f^m} \prod ^{m-1}_{k=0} g (f^kx)$ yields an example of a dynamical zeta function. Such functions have unexpected analytic properties and interesting relations to the theory of dynamical systems, statistical mechanics, and the spectral theory of certain operators (transfer operators). The first part of this monograph presents a general ...

Dynamical Zeta Functions for Piecewise Monotone Maps of the Interval 2004, American Mathematical Society, Providence

ISBN-13: 9780821836019

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Dynamical Zeta Functions for Piecewise Monotone Maps of the Interval 1994, American Mathematical Society(RI)

ISBN-13: 9780821869918

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