Resumen de On the size of linearization domains

Xavier Buff, Carsten Lunde Petersen

• Assume is a holomorphic map fixing 0 with derivative ?, where 0 < |?| = 1. If ? is not a root of unity, there is a formal power series ff(z) = z + (z2) such that ff(? z) = f(ff(z)). This power series is unique and we denote by Rconv(f) [0,+8] its radius of convergence. We denote by Rgeom(f) the largest radius r [0, Rconv(f)] such that ff(D(0,r)) U. In this paper, we present new elementary techniques for studying the maps f Rconv(f) and f Rgeom(f). Contrary to previous approaches, our techniques do not involve studying the arithmetical properties of rotation numbers.