Dynamical zeta functions for piecewise monotone maps of the interval
著者
書誌事項
Dynamical zeta functions for piecewise monotone maps of the interval
（CRM monograph series, v. 4）
American Mathematical Society, c1994
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注記
Includes bibliographical references
Paging of reprint 2004: v, 62 p.
内容説明・目次
内容説明
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 introduction to this subject. The second part is a detailed study of the zeta functions associated with piecewise monotone maps of the interval $[0,1]$. In particular, Ruelle gives a proof of a generalized form of the Baladi-Keller theorem relating the poles of $\zeta (z)$ and the eigenvalues of the transfer operator. He also proves a theorem expressing the largest eigenvalue of the transfer operator in terms of the ergodic properties of $(M,f,g)$.
目次
An introduction to dynamical zeta functions Piecewise monotone maps Bibliography.
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