Author	Pilgrim, Kevin M. author
Title	Combinations of Complex Dynamical Systems [electronic resource] / by Kevin M. Pilgrim
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg, 2003
Connect to	http://dx.doi.org/10.1007/b14147
Descript	XII, 120 p. online resource

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 tame. The program is motivated by the dictionary between the theories of iterated rational maps and Kleinian groups

Introduction -- Preliminaries -- Combinations -- Uniqueness of combinations -- Decompositions -- Uniqueness of decompositions -- Counting classes of annulus maps -- Applications to mapping class groups. Examples -- Canonical decomposition theorem

1. Mathematics
2. Dynamics
3. Ergodic theory
4. Functions of complex variables
5. Global analysis (Mathematics)
6. Manifolds (Mathematics)
7. Mathematics
8. Functions of a Complex Variable
9. Dynamical Systems and Ergodic Theory
10. Global Analysis and Analysis on Manifolds