RELATIONS WITH A FIXED INTERVAL EXCHANGE TRANSFORMATION

Magali Jay (1)

1 AMU - Aix Marseille Université

We study the group of all interval exchange transformations (IETs). We show that for every IET S, there exists a dense open set of admissible IETs that share a relation with S. This is an extension of a result published by Dahmani, Fujiwara and Guirardel in 2013: the group generated by a generic pair of elements of IET([0;1[) is not free (assuming a suitable condition on the underlying permutation).

Mots clés: interval exchange transformations; free group of rank 2; interval exchange transformations with flips

Domaines: Théorie des groupes [math.GR]; Systèmes dynamiques [math.DS]

Magali Jay. RELATIONS WITH A FIXED INTERVAL EXCHANGE TRANSFORMATION. 2022. ⟨hal-03625740⟩