Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 34, 2009, 27-46
Queens College of the City University of New York, Department of Mathematics
Flushing, NY 11367-1597, U.S.A.; Yunping.Jiang 'at' qc.cuny.edu
Abstract. The term integrable asymptotically conformal at a point for a quasiconformal map defined on a domain is defined. Furthermore, we prove that there is a normal form for this kind attracting or repelling or super-attracting fixed point with the control condition under a quasiconformal change of coordinate which is also asymptotically conformal at this fixed point. The change of coordinate is essentially unique. These results generalize König's Theorem and Böttcher's Theorem in classical complex analysis. The idea in proofs is new and uses holomorphic motion theory and provides a new understanding of the inside mechanism of these two famous theorems too.
2000 Mathematics Subject Classification: Primary 37F99; Secondary 32H02.
Key words: Integrable asymptotically conformal fixed point, holomorphic motion, normal form.
Reference to this article: Y. Jiang: Asymptotically conformal fixed points and holomorphic motions. Ann. Acad. Sci. Fenn. Math. 34 (2009), 27-46.
Copyright © 2009 by Academia Scientiarum Fennica