Ergodicity of certain cylinder flows

Here we build on the result given in [P1] and extend those in [HL2] to functions which are k times differentiable a.e., k>1. For each k we give a class of irrational numbers S k such that the skew product extension defined by these functions is ergodic for irrational rotations by these numbers. In the second part of this paper we examine the cohomology of functions over the adding machine transformation, and produce extensions of results from [H1] and [HL3]. © 1991 Hebrew University.