Isabelle Liousse

activity

20062026

most cited

C^{1}

-actions of Baumslag-Solitar groups on

S^{1}

20 citations · 35 across the 11 of their papers we have counts for

collaborators

14 papers

math.GR2026

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…

math.DS2023

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…

math.GR2021★ 1 cited

Uniform simplicity for subgroups of piecewise continuous bijections of the unit interval

Nancy Guelman, Isabelle Liousse, Pierre Arnoux

Let $I = [0, 1)$ and $P C (I)$ [resp. $P C^{+} (I)$ ] be the quotient group of the group of all piecewise continuous [resp. piecewise continuous and orientation preservin…

math.GR2019

Uniform perfectness for Interval Exchange Transformations with or without Flips

Nancy Guelman, Isabelle Liousse

Let $G$ be the group of all Interval Exchange Transformations. Results of Arnoux-Fathi ([Arn81b]), Sah ([Sah81]) and Vorobets ([Vor17]) state that $G_{0}$ the subgr…

math.DS2019★ 3 cited

Reversible Maps and Products of Involutions in Groups of IETS

Nancy Guelman, Isabelle Liousse

An element $f$ of a group $G$ is reversible if it is conjugated in $G$ to its own inverse; when the conjugating map is an involution, $f$ is called strongly reversible. We describe…

math.DS2017

Distortion in groups of Affine Interval Exchange transformations

Nancy Guelman, Isabelle Liousse

In this paper, we study distortion in the group $A$ of Affine Interval Exchange Transformations (AIET). We prove that any distorted element $f$ of $A$ , has an ite…

math.DS2017

Any Baumslag-Solitar action on surfaces with a pseudo-Anosov element has a finite orbit

Nancy Guelman, Isabelle Liousse

We consider $f, h$ homeomorphims generating a faithful $B S (1, n)$ -action on a closed surface $S$ , that is, $h f h^{- 1} = f^{n}$ , for some $n \geq 2$ . According to \cite{GL}, after rep…

math.DS2014★ 2 cited

Burnside problem for groups of homeomorphisms of compact surfaces

Nancy Guelman, Isabelle Liousse

A group $Γ$ is said to be periodic if for any $g$ in $Γ$ there is a positive integer $n$ with $g^{n} = i d$ . We first prove that a finitely generated periodic group acting on the 2-sphe…

math.DS2011

Burnside problem for measure preserving groups of toral homeomorphisms and for 2-groups of toral homeomorphisms

Nancy Guelman, Isabelle Liousse

A group $G$ is said to be periodic if for any $g \in G$ there exists a positive integer $n$ with $g^{n} = i d$ . We prove that a finitely generated periodic group of homeomorphisms on the…

math.DS2010★ 20 cited

$C^{1}$ -actions of Baumslag-Solitar groups on $S^{1}$

Nancy Guelman, Isabelle Liousse

Let $B S (1, n) =< a, b ∣ ab a^{- 1} = b^{n} >$ be the solvable Baumslag-Solitar group, where $n \geq 2$ . It is known that B(1, n) is isomorphic to the group generated by the two affine m…

math.DS2010

Actions of Baumslag-Solitar groups on surfaces

Nancy Guelman, Isabelle Liousse

Let $B S (1, n) =< a, b ∣ ab a^{- 1} = b^{n} >$ be the solvable Baumslag-Solitar group, where $n \geq 2$ . It is known that BS(1,n) is isomorphic to the group generated by the two affi…

math.DS2007★ 8 cited

Rotation set and Entropy

Heber Enrich, Nancy Guelman, Audrey Larcanché +1

In 1991 Llibre and MacKay proved that if $f$ is a 2-torus homeomorphism isotopic to identity and the rotation set of $f$ has a non empty interior then $f$ has positive topological…

math.DS2007

Singular measures of circle homeomorphisms with two break points

Akhtam Dzhalilov, Isabelle Liousse, Dieter Mayer

Let $T_{f}$ be a circle homeomorphism with two break points $a_{b}, c_{b}$ and irrational rotation number $ϱ_{f}$ . Suppose that the derivative $D f$ of its lift $f$ is absolute…

math.DS2006★ 1 cited

Rotation numbers in Thompson-Stein groups and applications

Isabelle Liousse

We study the properties of rotation numbers for some groups of piecewise linear homeomorphisms of the circle. We use these properties to obtain results on PL rigidity, non isomorph…

Some elementary amenable subgroups of interval exchange transformations

Interval Exchange Transformations groups. Free actions and dynamics of virtually abelian groups

Uniform simplicity for subgroups of piecewise continuous bijections of the unit interval

Uniform perfectness for Interval Exchange Transformations with or without Flips

Reversible Maps and Products of Involutions in Groups of IETS

Distortion in groups of Affine Interval Exchange transformations

Any Baumslag-Solitar action on surfaces with a pseudo-Anosov element has a finite orbit

Burnside problem for groups of homeomorphisms of compact surfaces

Burnside problem for measure preserving groups of toral homeomorphisms and for 2-groups of toral homeomorphisms

C1-actions of Baumslag-Solitar groups on S1

Actions of Baumslag-Solitar groups on surfaces

Rotation set and Entropy

Singular measures of circle homeomorphisms with two break points

Rotation numbers in Thompson-Stein groups and applications

$C^{1}$ -actions of Baumslag-Solitar groups on $S^{1}$