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

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

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...

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Veröffentlicht in:Dynamical systems (London, England) England), 2013-12, Vol.28 (4), p.539-550
Hauptverfasser: Hernandez, Carlos Angosto, Lopez, Gabriel Soler
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
Dynamical systems
flip
interval exchange transformation
Intervals
Keane-condition
minimality
Operators
orbit
Orbits
Primary 37E05
Rauzy-Veech algorithm
Secondary 37Bxx
Theorems
Transformations
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Zusammenfassung: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.
ISSN:1468-9367
1468-9375
DOI:10.1080/14689367.2013.824950