Linéarisation des germes de difféomorphismes holomorphes de (C,0). (Linearization of germs of holomorphic diffeomorphisms of (C,0)). (French) Zbl 0668.58010

Yoccoz, Jean-Christophe

C. R. Acad. Sci., Paris, Sér. I 306, No. 1, 55-58 (1988).

This paper announces the determination of the set of all a in \(S^ 1\) such that each germ of a holomorphic diffeomorphism on the complex plane of the form \(f(z)=az+O(z^ 2)\) is linearizable near 0. An essentially optimal estimate from below for the radius of convergence of the linearizing transformation is given. The proof is outlined.

Reviewer: P.Michor

MSC:

58D99	Spaces and manifolds of mappings (including nonlinear versions of 46Exx)
30D20	Entire functions of one complex variable (general theory)

Keywords:

holomorphic diffeomorphism on the complex plane