Nonorientable recurrence of flows and interval exchange transformations

Dynamics of Interval Exchange Transformations and Teichmüller Flows

Weak Mixing for Interval Exchange Transformations and Translation Flows

We show that a typical interval exchange transformation is either weakly mixing or it is an irrational rotation. We also conclude that a typical translation flow on a surface of genus g ≥ 2 (with prescribed singularity types) is weakly mixing.

Interval Exchange Transformations and Some Special Flows Are Not Mixing

An interval exchange transformation (I.E.T.) is a map of an interval into itself which is one-to-one and continuous except for a finite set of points and preserves Lebesgue measure. We prove that any I.E.T. is not mixing with respect to any Borel invariant measure. The same is true for any special flow constructed by any I.E.T. and any "roof" function of bounded variation. As an application of ...

Eigenvalues and Simplicity of Interval Exchange Transformations

In this paper we consider a class of d-interval exchange transformations, which we call the symmetric class. For this class we define a new self-dual induction process in which the system is successively induced on a union of sub-intervals. This algorithm gives rise to an underlying graph structure which reflects the dynamical behavior of the system, through the Rokhlin towers of the induced ma...

Languages of k-interval exchange transformations

This paper gives a complete characterization of those sequences of subword complexity (k− 1)n + 1 that are natural codings of orbits of k-interval exchange transformations, thereby answering an old question of Rauzy.