A priori bounds for GIETs, affine shadows and rigidity of foliations in genus two

S Ghazouani, C Ulcigrai - Publications mathématiques de l'IHÉS, 2023 - Springer
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 …

[HTML][HTML] Rigidity for piecewise smooth homeomorphisms on the circle

K Cunha, D Smania - Advances in Mathematics, 2014 - Elsevier
We find conditions for two piecewise C 2+ ν homeomorphisms f and g of the circle to be C 1
conjugate. Besides the restrictions on the combinatorics of the maps (we assume that the …

Renormalization conjecture and rigidity theory for circle diffeomorphisms with breaks

K Khanin, S Kocić - Geometric and Functional Analysis, 2014 - Springer
We prove the renormalization conjecture for circle diffeomorphisms with breaks, ie, that the
renormalizations of any two C 2+ α-smooth (α∈(0, 1)) circle diffeomorphisms with a break …

Singular continuous phase for Schrödinger operators over circle maps

S Kocić - Mathematische Annalen, 2024 - Springer
We consider a class of Schrödinger operators—referred to as Schrödinger operators over
circle maps—that generalize one-frequency quasiperiodic Schrödinger operators, with a …

-rigidity of circle maps with breaks for almost all rotation numbers

K Khanin, S Kocić, E Mazzeo - Annales scientifiques de l'École …, 2017 - numdam.org
R.–Nous démontrons que pour presque tous les irrationnels 2. 0; 1/, deux
difféomorphismes du cercle C2Clisses, 2. 0; 1/, avec un point de singularité de type rupture …

Generic rigidity for circle diffeomorphisms with breaks

S Kocić - Communications in Mathematical Physics, 2016 - Springer
We prove that C^ r C r-smooth (r> 2 r> 2) circle diffeomorphisms with a break, ie, circle
diffeomorphisms with a single singular point where the derivative has a jump discontinuity …

Rigidity for piecewise smooth circle homeomorphisms and certain GIETs

P Berk, F Trujillo - Advances in Mathematics, 2024 - Elsevier
In this article, we prove a rigidity property for a class of generalized interval exchange
transformations (GIETs), which contains the class of piecewise smooth circle …

Teichmüller dynamics, dilation tori and piecewise affine circle homeomorphisms

S Ghazouani - Communications in Mathematical Physics, 2021 - Springer
We study the coarse geometry of the moduli space of dilation tori with two singularities and
the dynamical properties of the action of the Teichmüller flow on this moduli space. This …

Renormalization of circle diffeomorphisms with a break-type singularity

H Akhadkulov, MSM Noorani, S Akhatkulov - arXiv preprint arXiv …, 2015 - arxiv.org
Let $ f $ be an orientation-preserving circle diffeomorphism with irrational rotation number
and with a break point $\xi_ {0}, $ that is, its derivative $ f'$ has a jump discontinuity at this …

Une invitation aux surfaces de dilatation

S Ghazouani - Séminaire de théorie spectrale et géométrie, 2019 - numdam.org
Une invitation aux surfaces de dilatation Page 1 Institut Fourier — Université de Grenoble I
Actes du séminaire de Théorie spectrale et géométrie Selim GHAZOUANI Une invitation …