no. 7
Robust local Hölder rigidity of circle maps with breaks
Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 7, pp. 1827-1845.

We prove that, for every ε∈(0,1), every two C2+α-smooth (α>0) circle diffeomorphisms with a break point, i.e. circle diffeomorphisms with a single singular point where the derivative has a jump discontinuity, with the same irrational rotation number ρ∈(0,1) and the same size of the break c∈R+\{1}, are conjugate to each other via a conjugacy which is (1−ε)-Hölder continuous at the break points. An analogous result does not hold for circle diffeomorphisms even when they are analytic.

DOI : 10.1016/j.anihpc.2018.03.003
Mots clés : Rigidity, Conjugacy, Circle maps with breaks 
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Khanin, Konstantin; Kocić, Saša. Robust local Hölder rigidity of circle maps with breaks. Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 7, pp. 1827-1845. doi : 10.1016/j.anihpc.2018.03.003. http://www.numdam.org/articles/10.1016/j.anihpc.2018.03.003/

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