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Minimality of interval exchange transformations with restrictions. (English) Zbl 1409.37048

M. Keane [Math. Z. 141, 25–31 (1975; Zbl 0278.28010)] showed that minimality is generic for irreducible interval exchange transformations (IETs). However, there are families of irreducible non-generic IETs where all or almost all of the IETs are not minimal.
The paper introduces poor and rich restriction spaces and the notion of stability for minimal IETs with restrictions. The authors prove that minimal uniquely ergodic IETs with poor restrictions are always stably minimal. They also conjecture that minimal IETs with rich restrictions are never stably minimal and that minimality occurs with probability 0 with rich restrictions.

MSC:

37E05 Dynamical systems involving maps of the interval
37E35 Flows on surfaces

Citations:

Zbl 0278.28010
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References:

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