Frontiers in complex dynamics : in celebration of John Milnor's 80th birthday / edited by Araceli Bonifant, Mikhail Lyubich, and Scott Sutherland.

Format:

Book

Author/Creator:

Bonifant, Araceli, author.

Contributor:

Bonifant, Araceli.

Lyubich, Mikhail.

Sutherland, Scott.

Series:

Princeton Mathematical Series

Language:

English

Subjects (All):

Milnor, John W. (John Willard), 1931-.

Milnor, John W.

Functions of complex variables.

Differentiable dynamical systems.

Physical Description:

1 online resource (824 p.)

Edition:

Course Book

Place of Publication:

Princeton, New Jersey ; Oxfordshire, England : Princeton University Press, 2014.

Language Note:

English

Summary:

John Milnor, best known for his work in differential topology, K-theory, and dynamical systems, is one of only three mathematicians to have won the Fields medal, the Abel prize, and the Wolf prize, and is the only one to have received all three of the Leroy P. Steele prizes. In honor of his eightieth birthday, this book gathers together surveys and papers inspired by Milnor's work, from distinguished experts examining not only holomorphic dynamics in one and several variables, but also differential geometry, entropy theory, and combinatorial group theory. The book contains the last paper written by William Thurston, as well as a short paper by John Milnor himself. Introductory sections put the papers in mathematical and historical perspective, color figures are included, and an index facilitates browsing. This collection will be useful to students and researchers for decades to come. The contributors are Marco Abate, Marco Arizzi, Alexander Blokh, Thierry Bousch, Xavier Buff, Serge Cantat, Tao Chen, Robert Devaney, Alexandre Dezotti, Tien-Cuong Dinh, Romain Dujardin, Hugo García-Compeán, William Goldman, Rotislav Grigorchuk, John Hubbard, Yunping Jiang, Linda Keen, Jan Kiwi, Genadi Levin, Daniel Meyer, John Milnor, Carlos Moreira, Vincente Muñoz, Viet-Anh Nguyên, Lex Oversteegen, Ricardo Pérez-Marco, Ross Ptacek, Jasmin Raissy, Pascale Roesch, Roberto Santos-Silva, Dierk Schleicher, Nessim Sibony, Daniel Smania, Tan Lei, William Thurston, Vladlen Timorin, Sebastian van Strien, and Alberto Verjovsky.

Contents:

Front matter

Contents

Preface

Introduction

Part I. One Complex Variable

Arithmetic of Unicritical Polynomial Maps / Milnor, John

Les racines des composantes hyperboliques de M sont des quarts d'entiers algébriques / Bousch, Thierry

Dynamical cores of topological polynomials / Blokh, Alexander / Oversteegen, Lex / Ptacek, Ross / Timorin, Vladlen

The quadratic dynatomic curves are smooth and irreducible / Bu, Xavier / Lei, Tan

Multicorns are not path connected / Hubbard, John Hamal / Schleicher, Dierk

Leading monomials of escape regions / Kiwi, Jan

Limiting behavior of Julia sets of singularly perturbed rational maps / Devaney, Robert L.

On (non-)local connectivity of some Julia sets / Dezotti, Alexandre / Roesch, Pascale

Perturbations of weakly expanding critical orbits / Levin, Genadi

Unmating of rational maps: Sufficient criteria and examples / Meyer, Daniel

A framework toward understanding the characterization of holomorphic dynamics / Jiang, Yunping

Part II. One Real Variable

Metric stability for random walks (with applications in renormalization theory) / Moreira, Carlos Gustavo / Smania, Daniel

Milnor's conjecture on monotonicity of topological entropy: Results and questions / Strien, Sebastian van

Entropy in dimension one / Thurston, William P.

Part III. Several Complex Variables

On Écalle-Hakim's theorems in holomorphic dynamics / Arizzi, Marco / Raissy, Jasmin

Index theorems for meromorphic self-maps of the projective space / Abate, Marco

Dynamics of automorphisms of compact complex surfaces / Cantat, Serge

Bifurcation currents and equidistribution in parameter space / Dujardin, Romain

Part IV. Laminations and Foliations

Entropy for hyperbolic Riemann surface laminations I / Dinh, Tien-Cuong / Nguyên, Viet-Anh / Sibony, Nessim

Entropy for hyperbolic Riemann surface laminations II / Dinh, Tien-Cuong / Nguyên, Viet-Anh / Sibony, Nessim

Intersection theory for ergodic solenoids / Muñoz, Vicente / Pérez-Marco, Ricardo

Invariants of four-manifolds with flows via cohomological field theory / García-Compeán, Hugo / Santos-Silva, Roberto / Verjovsky, Alberto

Color Plates

Part V. Geometry and Algebra

Two papers which changed my life: Milnor's seminal work on at manifolds and bundles / Goldman, William M.

Milnor's problem on the growth of groups and its consequences / Grigorchuk, Rostislav

Contributors

Index

Notes:

Description based upon print version of record.

Includes bibliographical references at the end of each chapters and index.

Description based on print version record.

ISBN:

1-4008-5139-4

1-4008-5131-9

OCLC:

871190735