Rotation number and one-parameter families of circle diffeomorphisms
- 1 June 1992
- journal article
- research article
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 12 (2) , 359-363
- https://doi.org/10.1017/s0143385700006805
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.Keywords
This publication has 4 references indexed in Scilit:
- A measure on the space of smooth mappings and dynamical system theoryJournal of the Mathematical Society of Japan, 1992
- Conjugaison différentiable des difféomorphismes du cercle dont le nombre de rotation vérifie une condition diophantienneAnnales Scientifiques de lʼÉcole Normale Supérieure, 1984
- Sur la Conjugaison Différentiable des Difféomorphismes du Cercle a des RotationsPublications mathématiques de l'IHÉS, 1979
- Small denominators. I. Mappings of the circumference onto itselfPublished by American Mathematical Society (AMS) ,1965