Robust local Hölder rigidity of circle maps with breaks

  • Konstantin Khanin

    Dept. of Math., University of Toronto, 40 St. George St., Toronto, ON, M5S 2E4, Canada
  • Saša Kocić

    Dept. of Math., University of Mississippi, P. O. Box 1848, University, MS 38677-1848, USA
Robust local Hölder rigidity of circle maps with breaks cover
Download PDF

A subscription is required to access this article.

Abstract

We prove that, for every ε(0,1)\varepsilon \in (0,1), every two C2+αC^{2 + \alpha }-smooth (α>0)(\alpha > 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)\rho \in (0,1) and the same size of the break c \in \mathbb{R}_{ + }\\{1\}, are conjugate to each other via a conjugacy which is (1ε)(1−\varepsilon )-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. 1827–1845

DOI 10.1016/J.ANIHPC.2018.03.003