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Frontiers in Complex Dynamics – In Celebration of John Milnor's 80th Birthday - Princeton Scholarship Online
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Frontiers in Complex Dynamics: In Celebration of John Milnor's 80th Birthday

Araceli Bonifant, Misha Lyubich, and Scott Sutherland

Abstract

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 writt ... More

Keywords: John Milnor, differential topology, K-theory, dynamical systems, holomorphic dynamics, differential geometry, entropy theory, combinatorial group theory, William Thurston

Bibliographic Information

Print publication date: 2014 Print ISBN-13: 9780691159294
Published to Princeton Scholarship Online: October 2017 DOI:10.23943/princeton/9780691159294.001.0001

Authors

Affiliations are at time of print publication.

Araceli Bonifant, author
University of Rhode Island

Misha Lyubich, author
Stony Brook University

Scott Sutherland, author
Stony Brook University

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Contents

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Front Matter

Title Pages

Preface

Introduction

Part I One Complex Variable

Arithmetic of Unicritical Polynomial Maps

John Milnor

Les racines des composantes hyperboliques de M sont des quarts d'entiers algébriques

Thierry Bousch

Dynamical cores of topological polynomials

Alexander Blokh, Lex Oversteegen, Ross Ptacek, and Vladlen Timorin

The quadratic dynatomic curves are smooth and irreducible

Xavier Buff and Tan Lei

Multicorns are not path connected

John Hamal Hubbard and Dierk Schleicher

Leading monomials of escape regions

Jan Kiwi

Limiting behavior of Julia sets of singularly perturbed rational maps

Robert L. Devaney

On (non-)local connectivity of some Julia sets

Alexandre Dezotti and Pascale Roesch

Perturbations of weakly expanding critical orbits

Genadi Levin

Unmating of rational maps: Sufficient criteria and examples

Daniel Meyer

A framework toward understanding the characterization of holomorphic dynamics

Yunping Jiang

Part II One Real Variable

Metric stability for random walks (with applications in renormalization theory)

Carlos Gustavo Moreira and Daniel Smania

Milnor's conjecture on monotonicity of topological entropy: Results and questions

Sebastian van Strien

Entropy in dimension one

William P. Thurston

Part III Several Complex Variables

On Ecalle-Hakim 's theorems in holomorphic dynamics

Marco Arizzi and Jasmin Raissy

Index theorems for meromorphic self-maps of the projective space

Marco Abate

Dynamics of automorphisms of compact complex surfaces

Serge Cantat

Bifurcation currents and equidistribution in parameter space

Romain Dujardin

Part IV Laminations and Foliations

Entropy for hyperbolic Riemann surface laminations I

Tien-Cuong Dinh, Viet-Anh Nguyên, and Nessim Sibony

Entropy for hyperbolic Riemann surface laminations II

Tien-Cuong Dinh, Viet-Anh Nguyên, and Nessim Sibony

Intersection theory for ergodic solenoids

Vicente Muñoz and Ricardo Pèrez-Marco

Invariants of four-manifolds with flows via cohomological field theory

Hugo García-Compeán, Roberto Santos-Silva, and Alberto Verjovsky

Part V Geometry and Algebra

Two papers which changed my life: Milnor's seminal work on flat manifolds and bundles

William M. Goldman

Mil nor's problem on the growth of groups and its consequences

Rostislav Grigorchuk

End Matter

Contributors

Index