Ergodic Theory and Dynamical Systems

Piece-wise affine maps conjugate to interval exchanges

a1 IMECC/Unicamp - CX.P 6065, CEP 13083-970, Campinas-SP, Brazil (e-mail: [email protected])


If T is an interval exchange transformation we denote by C_{{\rm aff}}(T) (respectively S_{{\rm aff}}(T)) the set of piece-wise affine maps of the interval which are conjugate (respectively semi-conjugate) to T. In this work we will give a description of the set C_{{\rm aff}}(T) for almost all T. We present an explicit interval exchange T_0 such that S_{{\rm aff}}(T_0)\backslash C_{{\rm aff}}(T_0) is non-empty. All the elements of S_{{\rm aff}}(T_0)\backslash C_{{\rm aff}}(T_0) are uniquely ergodic and have a unique wandering interval.

(Received May 19 1999)
(Revised April 3 2001)