Uniqueness of dynamical zeta functions and symmetric products

Abstract

A characterization of dynamically defined zeta functions is presented. It comprises a list of axioms, natural extension of the one which characterizes topological degree, and a uniqueness theorem. Lefschetz zeta function is the main (and proved unique) example of such zeta functions. Another interpretation of this function arises from the notion of symmetric product from which some corollaries and applications are obtained.