Title
Complex Analytic Dynamics on the Riemann Sphere
Abstract
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).
Related to
Institute for Mathematics and Its Applications>IMA Preprints Series
Suggested Citation
Blanchard, Paul.
(1984).
Complex Analytic Dynamics on the Riemann Sphere.
Retrieved from the University of Minnesota Digital Conservancy,
https://hdl.handle.net/11299/4989.