Minimality and the Rauzy – Veech algorithm for interval exchange transformations with flips

Abstract

Oriented interval exchange transformations (i.e.t.s) admitting infinite orbit of the Rauzy–Veech operator are minimal. In this paper, we analyse what happens for non-oriented i.e.t.s. In particular, we prove an analogous result for i.e.t.s with flips (Theorem A). We also show that the behaviour of i.e.t.s with flips is different to the one of oriented i.e.t.s, see Proposition 11.

Keywords:

• interval exchange transformation
• flip
• orbit
• minimality
• Keane-condition
• Rauzy-Veech algorithm

2000 Mathematics Subject Classification:

• Primary 37E05
• 37E10
• Secondary 37Bxx

Acknowledgements

The research was supported for the first named author by project MTM2011-25377 and for the second named author by project MTM2011-23221; both are projects of the Spanish Ministry of Science and Innovation. The second author was also supported by grant 08667/PI/08 of Fundación Séneca (Comunidad Autónoma de la Región de Murcia, Spain).