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Rotation number and one-parameter families of circle diffeomorphisms
Published online by Cambridge University Press: 19 September 2008
Abstract
We consider one-parameter families of circle diffeomorphisms, f1(x) = f(x) + t(t ∈ S1), where f: S1 is a Cr-diffeomorphism (r≥3). We show that, for Lebesgue almost every t ∈ S1 the rotation number of f1, is either a rational number or an irrational number of Roth type. In the former case, f1, has periodic orbits and, in the latter case, f1, is Cr − 2-conjugate to an irrational rigid rotation from well-known theorems of Herman and Yoccoz.
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