Expansive subdynamics for algebraic Z^d-actions.

Abstract

A general framework for investigating topological actions of Z^d on compact metric spaces was proposed by Boyle and Lind in terms of expansive behavior along lower dimensional subspaces of R^d. Here we completely describe this expansive behavior for the class of Z^d-actions given by commuting automorphisms of compact abelian groups. The description uses the logarithmic image of an algebraic variety together with a directional version of Noetherian modules over the ring of Laurent polynomials in several commuting variables.