## 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 C^{1} - part of Herman's theorem: if f is a C^{3} diffeomorphism of the circle to itself with a rotation number ω in this class, then f is C^{1} --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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