Dynamical zeta functions (Q2778783)

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].