Annales Academi� Scientiarum Fennic�
Mathematica
Volumen 34, 2009, 27-46

ASYMPTOTICALLY CONFORMAL FIXED POINTS AND HOLOMORPHIC MOTIONS

Yunping Jiang

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 K�nig's Theorem and B�ttcher'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.

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