Titlebook: Complex Dynamics; Lennart Carleson,Theodore W. Gamelin Textbook 1993 Springer-Verlag New York, Inc. 1993 integral.iteration.quasiconformal

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Springer-Handbuch der Mathematik IIIWe focus on the behavior of a rational function .(.) on the Fatou set F. Our aim is twofold: to show that every component of F is iterated eventually to a periodic component, and to classify the action of .(.) on periodic components.

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Springer-Handbuch der Mathematik IVCritical points and their forward orbits play a key role in complex dynamical systems. The forward orbit of the critical points is dense in the boundary of any Siegel disk and Herman ring. If the critical points and their iterates stay away from the Julia set, the mapping is expanding on the Julia set, and the Julia set becomes more tractable.

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Springer-Handbuch der Mathematik IVOne of the basic ideas behind the use of quasiconformal mappings is to consider two dynamical systems acting in different parts of the plane and to construct a new system that combines the dynamics of both. This procedure is called ..

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Critical Points and Expanding Maps,Critical points and their forward orbits play a key role in complex dynamical systems. The forward orbit of the critical points is dense in the boundary of any Siegel disk and Herman ring. If the critical points and their iterates stay away from the Julia set, the mapping is expanding on the Julia set, and the Julia set becomes more tractable.

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