We prove that, for every , every two -smooth 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 and the same size of the break , are conjugate to each other via a conjugacy which is -Hölder continuous at the break points. An analogous result does not hold for circle diffeomorphisms even when they are analytic.
Cite this article
Konstantin Khanin, Saša Kocić, Robust local Hölder rigidity of circle maps with breaks. Ann. Inst. H. Poincaré Anal. Non Linéaire 35 (2018), no. 7, pp. 1827–1845DOI 10.1016/J.ANIHPC.2018.03.003