Orbits for Products of Maps

Apisit Pakapongpun, Thomas Ward

Abstract

We study the behaviour of the dynamical zeta function and the orbit Dirichlet series for products of maps. The behaviour under products of the radius of convergence for the zeta function, and the abscissa of convergence for the orbit Dirichlet series, are discussed. The orbit Dirichlet series of the cartesian cube of a map with one orbit of each length is shown to have a natural boundary.