On SL(2,R) valued cocycles with zero exponents over Kronecker flows

We show that a generic SL(2, R) valued cocycle in the class of C(r), (0 < r < 1) cocycles based on a rotation flow on the d-torus, is either uniformly hyperbolic or has zero Lyapunov exponents provided that the components of winding vector gamma = (gamma(1), ..., gamma(d))of the rotation flow are rationally independent and satisfy the following super Liouvillian condition: vertical bar gamma(i) - p(n)(i)/q(n)vertical bar <= Ce(-qn1+delta), 1 <= i <= d, n is an element of N, where C > 0 and delta > 0 are some constants and p(n)(i), q(n) are some sequences of integers with q(n) -> infinity.