Complex Dynamics: Families and Friends / Edition 1

by Dierk Schleicher

Overview

Complex Dynamics: Families and Friends features contributions by many of the leading mathematicians in the field, such as Mikhail Lyubich, John Milnor, Mitsuhiro Shishikura, and William Thurston. Some of the chapters, including an introduction by Thurston to the general subject of complex dynamics, are classic manuscripts that were never published before but have influenced the field for more than two decades. Other chapters contain fresh, original work and bring readers to the current frontier of research. The title reflects the fruitful interplay between diverse mathematical fields bound together by the common theme of complex dynamics, including hyperbolic geometry, number theory, group theory, combinatorics, general dynamics, and many more. At the same time, the title alludes to the spirit of mathematical friendship among the researchers in this area. This book is a tribute to John Hubbard, one of the most inspiring pioneers in the field of complex dynamics.

Product Details

ISBN-13:	9781568814506
Publisher:	Taylor & Francis
Publication date:	11/03/2009
Pages:	663
Product dimensions:	6.20(w) x 9.20(h) x 1.50(d)

About the Author

Dierk Schleicher is a professor of mathematics at Jacobs University in Bremen, Germany.

Table of Contents

Polynomial Dynamics from Combinatorics to Topology. On the Geometry and Dynamics of Iterated Rational Maps. Appendix: Laminations, Julia Sets, and the Mandelbrot Set. Wandering Gaps for Weakly Hyperbolic Polynomials. Combinatorics of Polynomial Iterations. The Unicritical Branner-Hubbard Conjecture. A Priori Bounds for Some Infinitely Renormalizable Quadratics, III: Molecules. Beyond Polynomials: Rational and Transcendental Dynamics. The Connectivity of the Julia Set and Fixed Points. The Rabbit and Other Julia Sets Wrapped in Sierpinski Carpets. The Teichmuller Space of an Entire Function. Two Complex Dimensions. Cubic Polynomial Maps with Periodic Critical Orbit, Part I. Analytic Coordinates Recording Cubic Dynamics. Cubic Polynomials: A Measurable View of Parameter Space. Bifurcation Measure and Postcritically Finite Rational Maps. Real Dynamics of a Family of Plane Birational Maps: Trapping Regions and Entropy Zero. Making New Friends. The Hunt for Julia Sets with Positive Measure. On Thurston’s Pullback Map. On the Boundary Behavior of Thurston’s Pullback Map. Computing Arithmetic Invariants for Hyperbolic Reflection Groups.

What People are Saying About This

From the Publisher

The current volume is a collection of seventeen research articles, all of a very high standard. … give insight into the human side of Hubbard. The quality of the editing is superb, making this volume an absolute pleasure to read.
—Sebastian van Strien, Nieuw Archief voor Wiskunde, June 2012

In 2005 John Hamal Hubbard celebrated his sixtieth birthday. His families and friends organised a conference in his honour for him, for themselves, and for the mathematical community, especially those with an interest in complex dynamics in any shape or form. … [this volume] serves as a memento for the conference and much more. … For nearly thirty years, the preprint produced by Bill Thurston has been repeatedly photocopied (and, more recently, scanned). Here, it has been faithfully reproduced with discreet, but occasionally significant, well-judged editing by Dierk Schleicher and Nikita Selinger. Schleicher has also provided a crucial missing section: what he reckons would have been Thurston’s II.7. This spells out the way in which the quadratic laminations determine the topological dynamics on the corresponding Julia set in the cases when the Julia set is locally connected. … Thus, the first article of the book is the first full print version of a monograph that has been in existence since the early days … The illustrations are not only beautiful but also an important reminder of the role that pictures play in research in this field, and in the work of Hubbard and his students and co-workers in particular.
—Mary Rees, The Mathematical Intelligencer, 2011

Editorial Reviews

The current volume is a collection of seventeen research articles, all of a very high standard. … give insight into the human side of Hubbard. The quality of the editing is superb, making this volume an absolute pleasure to read.
—Sebastian van Strien, Nieuw Archief voor Wiskunde, June 2012

In 2005 John Hamal Hubbard celebrated his sixtieth birthday. His families and friends organised a conference in his honour for him, for themselves, and for the mathematical community, especially those with an interest in complex dynamics in any shape or form. … [this volume] serves as a memento for the conference and much more. … For nearly thirty years, the preprint produced by Bill Thurston has been repeatedly photocopied (and, more recently, scanned). Here, it has been faithfully reproduced with discreet, but occasionally significant, well-judged editing by Dierk Schleicher and Nikita Selinger. Schleicher has also provided a crucial missing section: what he reckons would have been Thurston’s II.7. This spells out the way in which the quadratic laminations determine the topological dynamics on the corresponding Julia set in the cases when the Julia set is locally connected. … Thus, the first article of the book is the first full print version of a monograph that has been in existence since the early days … The illustrations are not only beautiful but also an important reminder of the role that pictures play in research in this field, and in the work of Hubbard and his students and co-workers in particular.
—Mary Rees, The Mathematical Intelligencer, 2011

From the Publisher