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