Dynamical zeta functions
type: Item
instance of: scholarly article
zbMATH Open document ID: 0994.37013
author: Mark Pollicott
publication date: 2002-09-27T00:00:00Z
Mathematics Subject Classification ID: 37C30
Mathematics Subject Classification ID: 37D20
Mathematics Subject Classification ID: 37A25
zbMATH DE Number: 1722411
zbMATH Keywords: dynamical zeta functions
zbMATH Keywords: transfer operator
zbMATH Keywords: well-written survey
zbMATH Keywords: axiom A diffeomorphisms and flows
MaRDI profile type: Publication
title: Dynamical zeta functions
review text: Adapting the Hasse-Weil zeta function from algebraic geometry, Artin and Mazur introduced the first dynamical zeta function for a selfmap on a compact manifold. The paper under review is a well-written survey on the development of dynamical zeta functions since Artin-Mazur, with an emphasis on Axiom A diffeomorphisms and flows. An excellent complement to this paper is the recent article by D. Ruelle [Notices Am. Math. Soc. 49, 887-895 (2002)]. For a more topological approach, see the monograph by \textit{A. Fel'shtyn} [Dynamical zeta functions, Nielsen theory and Reidemeister torsion, Mem. Am. Math. Soc. 699 (2000; Zbl 0963.55002)].NEWLINENEWLINEFor the entire collection see [Zbl 0973.00044].
reviewed by: Peter Wong
description: scientific article; zbMATH DE number 1722411