Remarks on step cocycles over rotations, centralizers and coboundaries

Jean-Pierre Conze, Jonathan Marco

By using a cocycle generated by the step function ${\phi }_{\beta ,\gamma }=1_{[0,\beta ]}-1_{[0,\beta ]}(.+\gamma )$ over an irrational rotation $x\to x+\alpha \mathrm{mod}1$, we present examples which illustrate…