Abstract
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) |
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Pages (from-to) | 125-147 |
Number of pages | 23 |
Journal | Colloquium Mathematicum |
Volume | 136 |
Issue number | 1 |
DOIs | |
State | Published - 2014 |
All Science Journal Classification (ASJC) codes
- General Mathematics