Herman's theory revisited
Abstract
We prove that a $C^{2+\alpha}$smooth orientationpreserving circle diffeomorphism with rotation number in Diophantine class $D_\delta$, $0<\delta<\alpha\le1$, is $C^{1+\alpha\delta}$smoothly conjugate to a rigid rotation. We also derive the most precise version of Denjoy's inequality for such diffeomorphisms.
 Publication:

Inventiones Mathematicae
 Pub Date:
 May 2009
 DOI:
 10.1007/s002220090200z
 arXiv:
 arXiv:0707.0075
 Bibcode:
 2009InMat.178..333K
 Keywords:

 Mathematics  Dynamical Systems;
 37E10
 EPrint:
 10 pages