This work is a research-level monograph whose goal is to develop a general combination, decomposition, and structure theory for branched coverings of the two-sphere to itself, regarded as the combinatorial and topological objects which arise in the classification of certain holomorphic dynamical systems on the Riemann sphere. It is intended for researchers interested in the classification of those complex one-dimensional dynamical systems which are in some loose sense <EM>tame. The program is motivated by the dictionary between the theories of iterated rational maps and Kleinian groups.
Lecture Notes in Mathematics Editors: J.--M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris 1827 3 Berlin Heidelberg New York Hong Kong London Milan Paris Tokyo Kevin M. Pilgrim Combinations of Complex Dynamical Systems 13 Author Kevin M. Pilgrim Department of Mathematics Indiana University Bloomington, IN 47401, USA e-mail:
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