A CLT for cocycles over rotations

We will present an instance of the central limit theorem in entropy zero dynamics obtained as a temporal limit theorem. We consider deterministic random walks on the real line R driven by a rotations (or in other words, a skew product over an irrational rotation) and prove a temporal CLT for badly approximable rotation numbers and piecewise cocycle with jumps at certain irrational values. This generalizes previous results by J.Beck and by D. Dolgopyat and O. Sarig. The proof uses continued fraction and Ostrowsky renormalization. The talk is based on joint work with Michael Bromberg.