Typical dynamics associated to rings of S-integers
by
Thomas Ward
University of East Anglia

We describe a construction of a family of isometric extensions of familiar hyperbolic dynamical systems (like toral automorphisms, full shifts, certain algebraic CA maps). The extensions are parametrised by a probability space, and within this space the typical behaviour is predicted using classical number- theoretic conjectures and an ergodic map on the parameter space itself. Using Heath-Brown's work on the Artin conjectures, the typical behaviour can (usually) be described exactly in the case where the base map is a full shift.

Date received: February 23, 1998