Abstract
In this Thesis we investigate interval translation maps (ITMs) with, on the circle, two intervals, also known as “double rotations”. ITMs are either of finite or infinite type. If they are of finite type they reduce to interval exchange-transformations (IETs). It is argued that by using the induction procedure described by Suzuki et al, we can demonstrate several properties of double rotations. We show that almost every double rotation is of finite type, with respect to Lebesgue measure. Further we show that a typical double rotation is uniquely ergodic. Next we consider complexity. It is trivially true that, in the case of IETs complexity is linear. However, contrary to expectation, there are double rotations with super-linear complexity. Finally we give approximations for the dimension of the set of all infinite double rotations.