Combinations of Complex Dynamical Systems
Pilgrim, Kevin M.
Combinations of Complex Dynamical Systems [electronic resource] / by Kevin M. Pilgrim. - XII, 120 p. online resource. - Lecture Notes in Mathematics, 1827 0075-8434 ; . - Lecture Notes in Mathematics, 1827 .
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.
9783540399360
10.1007/b14147 doi
Functions of complex variables.
Differentiable dynamical systems.
Global analysis.
Functions of a Complex Variable.
Dynamical Systems and Ergodic Theory.
Global Analysis and Analysis on Manifolds.
QA331-355
515.9
Combinations of Complex Dynamical Systems [electronic resource] / by Kevin M. Pilgrim. - XII, 120 p. online resource. - Lecture Notes in Mathematics, 1827 0075-8434 ; . - Lecture Notes in Mathematics, 1827 .
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.
9783540399360
10.1007/b14147 doi
Functions of complex variables.
Differentiable dynamical systems.
Global analysis.
Functions of a Complex Variable.
Dynamical Systems and Ergodic Theory.
Global Analysis and Analysis on Manifolds.
QA331-355
515.9