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.
Combinations of Complex Dynamical Systems
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Inside This Book
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First Sentence:
This work is about the combinatorial aspects of rigidity phenomena in complex dynamics. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
postcritical set, finite rational maps, quadratic rational maps, embellished map, annular edge, combinatorial equivalence, amalgamating data, gluing data, rational traps, rational neap, combinatorial classes, disk maps, mapping tree, hyperbolic components, mapping class group, missing disks, sphere maps, branched coverings, isotopy class, finite polynomials, finite maps, boundary components, local degrees Key Phrases - Capitalized Phrases (CAPs): (learn more)
Twist Theorem, Topological Compatibility Axiom, Proof of Uniqueness of Combinations Theorem New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
This work is about the combinatorial aspects of rigidity phenomena in complex dynamics. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
postcritical set, finite rational maps, quadratic rational maps, embellished map, annular edge, combinatorial equivalence, amalgamating data, gluing data, rational traps, rational neap, combinatorial classes, disk maps, mapping tree, hyperbolic components, mapping class group, missing disks, sphere maps, branched coverings, isotopy class, finite polynomials, finite maps, boundary components, local degrees Key Phrases - Capitalized Phrases (CAPs): (learn more)
Twist Theorem, Topological Compatibility Axiom, Proof of Uniqueness of Combinations Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 1
book:
34
books
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- Matrix Theory, Vol. 2 by Felix R. Gantmacher in Back Matter
- Big Queues (Lecture Notes in Mathematics) by Ayalvadi J. Ganesh in Back Matter
- Noncommutative Geometry: Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 3-9, 2000 (Lecture Notes in Mathematics / C.I.M.E. Foundation Subseries) by Alain Connes in Back Matter
- Gröbner Bases and the Computation of Group Cohomology (Lecture Notes in Mathematics) by David J. Green in Back Matter
- Multiscale Problems and Methods in Numerical Simulations: Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 9-15, ... Mathematics / C.I.M.E. Foundation Subseries) by James H. Bramble in Back Matter
- Random Times and Enlargements of Filtrations in a Brownian Setting (Lecture Notes in Mathematics) by Roger Mansuy in Back Matter
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