Conformal Dynamics and Hyperbolic Geometry
About this Title
Francis Bonahon, University of Southern California, Los Angeles, CA, Robert L. Devaney, Boston University, Boston, MA, Frederick P. Gardiner, Brooklyn College, CUNY, New York, NY and Dragomir Šarić, Graduate School and University Center of CUNY, New York, NY, Editors
Publication: Contemporary Mathematics
Publication Year 2012: Volume 573
ISBNs: 978-0-8218-5348-1 (print); 978-0-8218-9025-7 (online)
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 Teichmüller theory, the geometry of Fuchsian and Kleinian groups, domain convergence properties for the Poincaré 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.
Graduate students and research mathematicians interested in conformal dynamics and hyperbolic geometry.
Table of Contents
- Michael Beck, Yunping Jiang and Sudeb Mitra – Normal families and holomorphic motions over infinite dimensional parameter spaces
- Reza Chamanara and Dragomir Šarić – Elementary moves and the modular group of the compact solenoid
- Laura DeMarco – Combinatorics and topology of the shift locus
- Robert L. Devaney – Dynamics of $z^n + \lambda /z^n$; Why the Case $n = 2$ is Crazy
- Clifford J. Earle and Albert Marden – On holomorphic families of Riemann surfaces
- Frederick P. Gardiner and Yunping Jiang – Circle Endomorphisms, Dual Circles and Thompson’s Group
- Jun Hu, Francisco G. Jimenez and Oleg Muzician – Rational maps with half symmetries, Julia sets, and Multibrot sets in parameter planes
- Nikola Lakic and Greg Markowsky – The rate of convergence of the hyperbolic density on sequences of domains.
- Sara Maloni – The asymptotic directions of pleating rays in the Maskit embedding.
- John Milnor. \\with an Appendix by A. Poirier – Hyperbolic components
- Christian Wolf – On barycenter entropy for rational maps
- Shenglan Yuan – Parameter Plane of a Family of Meromorphic Functions with Two Asymptotic Values