On ergodicity of p-adic dynamical systems for arbitrary prime p

Abstract

In this paper, we obtain necessary and sufficient conditions for ergodicity (with respect to the normalized Haar measure) of 1-Lipschitz p-adic functions that are defined on (and valuated in) the space ℤp of p-adic integers for any prime p. The conditions are stated in terms of coordinate representations of p-adic functions.