Dynamical zeta functions for piecewise monotone maps of the interval
Author(s)
Bibliographic Information
Dynamical zeta functions for piecewise monotone maps of the interval
（CRM monograph series, v. 4）
American Mathematical Society, c1994
Available at / 35 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
RUE||1||7200021326847
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
dc20:514/r8372070306204
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Note
Includes bibliographical references
Paging of reprint 2004: v, 62 p.
Description and Table of Contents
Description
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 $(M,f,g)$.
Table of Contents
An introduction to dynamical zeta functions Piecewise monotone maps Bibliography.
by "Nielsen BookData"