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.
• Physical Description: XII, 120 p. online resource.
• ISBN: 9783540399360
• ISSN: 0075-8434 ;
• DOI: 10.1007/b14147

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.