Pilgrim Combinations of Complex Dynamical Systems

Erscheinungsjahr 2003
ISBN: 978-3-540-39936-0
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 1827, 120 Seiten, eBook

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Pilgrim, Kevin M.

Inhaltsverzeichnis

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