7 citations · 15 across the 12 of their papers we have counts for
13 papers
Regularity of conjugacies of linearizable generalized interval exchange transformations
Selim Ghazouani, Corinna Ulcigrai
We consider generalized interval exchange transformations (GIETs) of d intervals () which are linearizable, i.e. differentiably conjugated to standard interval exchange ma…
Closed geodesics in dilation surfaces
Adrien Boulanger, Selim Ghazouani, Guillaume Tahar
We prove that directions of closed geodesics in every dilation surface form a dense subset of the circle. The proof draws on a study of the degenerations of the Delaunay triangulat…
A priori bounds for GIETs, affine shadows and rigidity of foliations in genus 2
Selim Ghazouani, Corinna Ulcigrai
We prove a rigidity result for foliations on surfaces of genus two, which can be seen as a generalization to higher genus of Herman's theorem on circle diffeomorphisms and, corresp…
-dynamics on the moduli space of one-holed tori
Adrien Boulanger, Selim Ghazouani
We study the -action on the moduli space of (triangulable) dilation tori with one boundary component. We prove that every orbit is either closed or dense…
The symplectic structure of renormalisation of circle diffeomorphisms with breaks
Selim Ghazouani, Konstantin Khanin
In this article we prove that iterated renormalisations of circle diffeomorphisms with breaks, , with given size of breaks, converge to an invariant family…
Local rigidity for periodic generalised interval exchange transformations
Selim Ghazouani
In this article we study local rigidity properties of generalised interval exchange maps using renormalisation methods. We study the dynamics of the renormalisation operator $\math…
Teichmüller dynamics, dilation tori and piecewise affine circle homeomorphisms
Selim Ghazouani
We study the coarse geometry of the moduli space of dilation tori with two singularities and the dynamical properties of the action of the Teichmuller flow on this moduli space. Th…
Cascades in the dynamics of affine interval exchange transformations
Adrien Boulanger, Charles Fougeron, Selim Ghazouani
We describe in this article the dynamics of a -parameter family of affine interval exchange transformations. It amounts to studying the directional foliations of a particular af…
Affine surfaces and their Veech groups
Eduard Duryev, Charles Fougeron, Selim Ghazouani
We introduce a class of objects which we call 'affine surfaces'. These provide families of foliations on surfaces whose dynamics we are interested in. We present and analyze a coup…
Mapping class group dynamics and the holonomy of branched affine structures
Selim Ghazouani
We classify, up to few exceptions, the orbit closures of the -action on the affine character variety . We obtain from this classificat…
Moduli spaces of flat tori and elliptic hypergeometric functions
Selim Ghazouani, Luc Pirio
In the genus one case, we make explicit some constructions of Veech on flat surfaces and generalize some geometric results of Thurston about moduli spaces of flat spheres as well a…
Moduli spaces of flat tori with prescribed holonomy
Selim Ghazouani, Luc Pirio
We generalise to the genus one case several results of Thurston concerning moduli spaces of flat Euclidean structures with conical singularities on the two dimensional sphere. More…
Mapping class group dynamics on Aff(C)-characters
Selim Ghazouani
We prove that in genus bigger than , the mapping class group action on -characters is ergodic. This implies that almost every representation $π_1 S \lo…