Bufetov’s questions on Rauzy induction and self-similar interval exchange transformations
Given an interval exchange transformation (IET) and a sub-interval, there arises a natural visitation matrix that relates the induced IET to the original IET. We show that the original IET, up to topological conjugacy, may be recovered from successive visitation matrices. This answers a question by A. Bufetov and generalizes work by W. A. Veech, which considered the case when the matrices arise from Rauzy induction.
The proof reduces to the case of self-similar IET’s, those in which the induced IET is equivalent to the original. We end by discussing other problems concerning such IET’s.
- Jon FICKENSCHER