Conformal dynamics and hyperbolic geometry : Conference on Conformal Dynamics and Hyperbolic Geometry in honor of Linda Keen's 70th birthday, Graduate School and University Center of CUNY New York, New York, October 21-23, 2010 / Francis Bonahon [and three others], editors.

Format:

Book

Contributor:

Keen, Linda, honouree.

Bonahon, Francis, 1955- editor.

Series:

Contemporary mathematics (American Mathematical Society). 0271-4132 573

Contemporary mathematics, 573 0271-4132

Language:

English

Subjects (All):

Geometric function theory--Congresses.

Geometric function theory.

Deformations (Mechanics)--Congresses.

Deformations (Mechanics).

Geometry, Hyperbolic--Congresses.

Geometry, Hyperbolic.

Physical Description:

1 online resource (266 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2012]

Language Note:

English

Summary:

This volume contains the proceedings of the Conference on Conformal Dynamics and Hyperbolic Geometry, held October 21-23, 2010, in honor of Linda Keen's 70th birthday. This volume provides a valuable introduction to problems in conformal and hyperbolic geometry and one dimensional, conformal dynamics. It includes a classic expository article by John Milnor on the structure of hyperbolic components of the parameter space for dynamical systems arising from the iteration of polynomial maps in the complex plane. In addition there are foundational results concerning Teichmuller theory, the geometry of Fuchsian and Kleinian groups, domain convergence properties for the Poincare metric, elaboration of the theory of the universal solenoid, the geometry of dynamical systems acting on a circle, and realization of Thompson's group as a mapping class group for a uniformly asymptotically affine circle endomorphism. The portion of the volume dealing with complex dynamics will appeal to a diverse group of mathematicians. Recently many researchers working in a wide range of topics, including topology, algebraic geometry, complex analysis, and dynamical systems, have become involved in aspects of this field.

Contents:

Preface

Normal families and holomorphic motions over infinite dimensional parameter spaces

1. Introduction

2. Proof of Theorem A

3. Group-equivariant extensions of holomorphic motions

4. Proof of Theorem B

References

Elementary moves and the modular group of the compact solenoid

2. The abstract commensurator of a surface group

3. Pants decompositions and subgroups of surface groups

4. Elementary moves and induced isomorphisms of finite index subgroups of

5. The isotropy group

6. Exact sequences

7. The center of is trivial

8. Relations in

Combinatorics and topology of the shift locus

2. The space of polynomials and the shift locus

3. Topological conjugacy, the pictograph, and shift automorphisms

4. The Branner-Hubbard slice

5. For further investigation

Dynamics of ⁿ+ / ⁿ - Why the Case =2 is Crazy Introduction

1. Elementary Mapping Properties

2. The McMullen domain

3. Mandelpinski Necklaces

6. Analytic Isomorphism between Hyperbolic Components On holomorphic families of Riemann surfaces

Circle Endomorphisms, Dual Circles and Thompson’s Group

Rational maps with half symmetries, Julia sets, and Multibrot sets in parameter planes

The rate of convergence of the hyperbolic density on sequences of domains.

The asymptotic directions of pleating rays in the Maskit embedding.

Hyperbolic components

On barycenter entropy for rational maps

Parameter Plane of a Family of Meromorphic Functions with Two Asymptotic Values

Notes:

Description based upon print version of record.

Includes bibliographical references.

Description based on print version record.

ISBN:

0-8218-9025-5