Eigenvalues and simplicity of interval exchange transformations

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.

Joinings of Three-interval Exchange Transformations

We show that among three-interval exchange transformations there exists a dichotomy: T has minimal self-joinings whenever the associated subshift is linearly recurrent, and is rigid otherwise. We build also a family of simple rigid three-interval exchange transformations, which is a step towards an old question of Veech, and a family of rigid three-interval exchange transformations which includ...

Dynamics of Interval Exchange Transformations and Teichmüller Flows

Unique Ergodicity of Circle and Interval Exchange Transformations with Flips

We study circle exchange transformations on three subintervals, that reverse orientation on at least one of the subintervals (a flip). We prove that if such a transformation has exactly one flip, then it has a periodic orbit and thus no dense orbit. For the cases of two and three flips, we construct uniquely ergodic minimal examples by finding a periodic point of an adapted Rauzy–Veech renormal...