20 citations · 35 across the 11 of their papers we have counts for
14 papers
Some elementary amenable subgroups of interval exchange transformations
Nancy Guelman, Isabelle Liousse
In this paper, we study a family of finitely generated elementary amenable iet-groups. These groups are generated by finitely many rationals iets and rotations. For them, we state…
Interval Exchange Transformations groups. Free actions and dynamics of virtually abelian groups
Nancy Guelman, Isabelle Liousse
Hölder's theorem states that any group acting freely by circle homeomorphisms is abelian, this is no longer true for interval exchange transformations: we first give examples of fr…
Uniform simplicity for subgroups of piecewise continuous bijections of the unit interval
Nancy Guelman, Isabelle Liousse, Pierre Arnoux
Let and [resp. ] be the quotient group of the group of all piecewise continuous [resp. piecewise continuous and orientation preservin…
Uniform perfectness for Interval Exchange Transformations with or without Flips
Nancy Guelman, Isabelle Liousse
Let be the group of all Interval Exchange Transformations. Results of Arnoux-Fathi ([Arn81b]), Sah ([Sah81]) and Vorobets ([Vor17]) state that the subgr…
Reversible Maps and Products of Involutions in Groups of IETS
Nancy Guelman, Isabelle Liousse
An element of a group is reversible if it is conjugated in to its own inverse; when the conjugating map is an involution, is called strongly reversible. We describe…
Distortion in groups of Affine Interval Exchange transformations
Nancy Guelman, Isabelle Liousse
In this paper, we study distortion in the group of Affine Interval Exchange Transformations (AIET). We prove that any distorted element of , has an ite…