Rational maps and Kleinian groups


What are the possible topological forms for a conformal dynamical system? Part of the answer is provided by two theorems, due to Thurston, which employ iteration on Teichmüller space to construct rational maps and Kleinian groups of a given topological form. More precisely, the iteration either finds a geometric model or reveals a topological obstruction to its existence. This dichotomy stems from:

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@inproceedings{McMullen1990RationalMA, title={Rational maps and Kleinian groups}, author={C. McMullen}, year={1990} }