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Piece-wise affine maps conjugate to interval exchanges

  • MILTON COBO (a1)
Abstract

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 allT. 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.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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