Combinations of Complex Dynamical Systems

• Main Author: Pilgrim, Kevin M. (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2003.
• Edition: 1st ed. 2003.
• Series: Lecture Notes in Mathematics, 1827
• Subjects: Functions of complex variables.; Dynamics.; Ergodic theory.; Global analysis (Mathematics).; Manifolds (Mathematics).; Functions of a Complex Variable.; Dynamical Systems and Ergodic Theory.; Global Analysis and Analysis on Manifolds.

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 sys...

Table of Contents:

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