Affiliation: College of Arts and Sciences, Department of Mathematics
For a fixed prime p, we examine the ergodic properties and orbit equivalence classes of transformations on the p-adic numbers. Approximations and constructions are given that aid in the understanding of the ergodic properties of the transformations. Transformation types are calculated to give examples of transformations on measure spaces in various orbit equivalence classes. Moreover, we study the behavior of orbit equivalence classes under iteration. Finally, we give some preliminary investigations into the Haar measure and Hausdorff dimension of p-adic Julia sets and possible representations of the Chacon map as a 3-adic transformation.