We consider special flows over the rotation on the circle by an irrational α under roof functions of bounded variation. The roof functions, in the Lebesgue decomposition, are assumed to have a continuous singular part coming from a quasi-similar Cantor set (including the devil’s staircase case). Moreover, a finite number of discontinuities is allowed. Assuming that has bounded partial quotients, we prove that all such flows are weakly mixing and enjoy the weak Ratner property. Moreover, we provide a sufficient condition on the roof function for stability of Ratner’s cocycle property of the resulting special flow.
|Original language||English (US)|
|Number of pages||23|
|State||Published - 2014|
All Science Journal Classification (ASJC) codes