Nouvelle preuve d'un théorème de Yoccoz

Abstract

If θ is an irrational real number such that ∑(ln q n+1 )/ q n =+∞ where p n / q n are the convergents of θ, then the quadratic polynomial P θ(z)= e i 2πθ z+z 2 is not linearizable at 0. This theorem has been proved in 1988 by J.C. Yoccoz, who first constructs a nonlinearizable germ by inverting a renormalisation procedure, and then proves universality of the quadratic family for that question. We give an alternative proof, based on the study of the explosion of parabolic cycles. To cite this article: A. Chéritat, C. R. Acad. Sci. Paris, Ser. I 338 (2004).