Ergodicity of cocyles over 2-dimensional rotations

Abstract

We study recurrence and ergodicity of cocycles with values in R d , d $\ge$ 1, over rotations by badly approximable irrational numbers on T $\rho$ , $\rho$ \> 1. The discontinuities of the functions generating the cocycles also satisfy a Diophantine condition. For simplicity of notation we mainly consider the cases $\rho$ = 2, d = 1 and 2.