The term integrable asymptotically conformal at a point for a quasiconformalmap defined on a domain is defined. Furthermore, we prove that there is anormal form for this kind attracting or repelling or super-attracting fixedpoint with the control condition under a quasiconformal change of coordinatewhich is also asymptotically conformal at this fixed point. The change ofcoordinate is essentially unique. These results generalize K\"onig's Theoremand B\"ottcher's Theorem in classical complex analysis. The idea in proofs isnew and uses holomorphic motion theory and provides a new understanding of theinside mechanism of these two famous theorems too.
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