Notes on Ergodic Theory in Infinite Measure Spaces

Abstract

This article is concerned with ergodic theory for transformations which preserve an infinite measure. In the first part we present an overview of the invertible case with a focus on weakly wandering sequences and their applications to number theory as it has developed over the last fifty years. The second part presents a very preliminary investigation into extending weakly wandering sequences to the non-invertible case. This consists primarily of a few examples which illustrate the complexities which arise in the non-invertible case.