Combinations of Complex Dynamical Systems [electronic resource] / by Kevin M. Pilgrim.

By: Pilgrim, Kevin M [author.]Contributor(s): SpringerLink (Online service)Material type: TextTextSeries: Lecture Notes in Mathematics ; 1827Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2003Description: XII, 120 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540399360Subject(s): Mathematics | Differentiable dynamical systems | Functions of complex variables | Global analysis | Mathematics | Functions of a Complex Variable | Dynamical Systems and Ergodic Theory | Global Analysis and Analysis on ManifoldsAdditional physical formats: Printed edition:: No titleDDC classification: 515.9 LOC classification: QA331-355Online resources: Click here to access online
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.
In: Springer eBooksSummary: 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.
Item type: E-BOOKS
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Introduction -- Preliminaries -- Combinations -- Uniqueness of combinations -- Decompositions -- Uniqueness of decompositions -- Counting classes of annulus maps -- Applications to mapping class groups. Examples -- Canonical decomposition theorem.

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.

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