Complex Analytic Dynamics on the Riemann Sphere

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Complex Analytic Dynamics on the Riemann Sphere

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1984

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Holomorphic, non-invertible dynamical systems of the Riemann sphere are surprisingly intricate and beautiful. Often the indecomposable, completely invariant sets are fractals (a la Mandelbrot [M1]) because, in fact, they are quasi-self-similar (see Sullivan [S3] and (8.5)). Sometimes they are nowhere differentiable Jordan curves whose Hausdorff dimension is greater than one (Sullivan [S4] and Ruelle [R]). Yet these sets are determined by a single analytic function zn+1 = R(zn).

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Blanchard, Paul. (1984). Complex Analytic Dynamics on the Riemann Sphere. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/4989.

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