Author | Pilgrim, Kevin M. author |
---|---|

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

Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 2003 |

Connect to | http://dx.doi.org/10.1007/b14147 |

Descript | XII, 120 p. online resource |

SUMMARY

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

CONTENT

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

Mathematics
Dynamics
Ergodic theory
Functions of complex variables
Global analysis (Mathematics)
Manifolds (Mathematics)
Mathematics
Functions of a Complex Variable
Dynamical Systems and Ergodic Theory
Global Analysis and Analysis on Manifolds