منابع مشابه
Holomorphic Motions and Normal Forms in Complex Analysis
We give a brief review of holomorphic motions and its relation with quasiconformal mapping theory. Furthermore, we apply the holomorphic motions to give new proofs of famous König’s Theorem and Böttcher’s Theorem in classical complex analysis.
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We develop an isotopy principle for holomorphic motions. Our main result concerns the extendability of a holomorphic motion h(t, z) of a finite subset E of the Riemann sphere C parameterized by a pointed hyperbolic Riemann surface (X, t0). We prove that if this holomorphic motion has a guiding quasiconformal isotopy, then it can be extended to a new holomorphic motion of E ∪ {p} for any point p...
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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 superattracting 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 essent...
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1 Background The theory of holomorphic motions, introduced by Mané-Sad-Sullivan [1] and advanced by Slodkowski [2], has had a significant impact on the theory of quasiconformal mappings. A reasonably thorough account of this is given in our book [3]. In [4, 5] we established some classical distortion theorems for quasiconformal mappings and used the theory to develop connections between Schottk...
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Rational maps are self-maps of the Riemann sphere of the form z → p(z)/q(z) where p(z) and q(z) are polynomials. Kleinian groups are discrete subgroups of PSL(2,C), acting as isometries of 3-dimensional hyperbolic space and as conformal automorphisms of its boundary, the Riemann sphere. Both theories experienced remarkable advances in the last two decades of the 20th century and are very active...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2018
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/14217