On obstacles for C^2 rigidity for circle maps with singularities. On obstacles for C^2 rigidity for circle maps with singularities

Konstantin Khanin

We shall present a general argument which explains why one cannot expect C^2 rigidity for circle maps with singularities. In the case of circle maps with breaks we show that for any irrational rotation number the conjugacy in general is not smoother than C^{2-δ} where delta is a universal constant which depends only on the size of a break.This result holds for maps which are arbitrarily smooth outside of their break points.

http://scgp.stonybrook.edu/video_portal/video.php?id=4701

Simons- Program: Renormalization and universality in Conformal Geometry, Dynamics, Random Processes, and Field Theory