Institute for Mathematical Sciences

Preprint ims90-13

J. J. P. Veerman and F. M. Tangerman
A Remark on Herman's Theorem for Circle Diffeomorphisms

Abstract: We define a class of real numbers that has full measure and is contained in the set of Roth numbers. We prove the C1 - part of Herman's theorem: if f is a C3 diffeomorphism of the circle to itself with a rotation number ω in this class, then f is C1 --conjugate to a rotation by ω. As a result of restrictiing the class of admissible rotation numbers, our proof is substantially shorter than Yoccoz' proof.
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