Frontiers in Complex Dynamics

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.

Autorentext

Edited by Araceli Bonifant, Misha Lyubich, & Scott Sutherland

Inhalt

• Frontmatter,
• Contents,
• Preface,
• Introduction,
• Arithmetic of Unicritical Polynomial Maps,
• Les racines des composantes hyperboliques de M sont des quarts d'entiers algébriques,
• Dynamical cores of topological polynomials,
• The quadratic dynatomic curves are smooth and irreducible,
• Multicorns are not path connected,
• Leading monomials of escape regions,
• Limiting behavior of Julia sets of singularly perturbed rational maps,
• On (non-)local connectivity of some Julia sets,
• Perturbations of weakly expanding critical orbits,
• Unmating of rational maps: Sufficient criteria and examples,
• A framework toward understanding the characterization of holomorphic dynamics,
• Metric stability for random walks (with applications in renormalization theory),
• Milnor's conjecture on monotonicity of topological entropy: Results and questions,
• Entropy in dimension one,
• On Écalle-Hakim's theorems in holomorphic dynamics,
• Index theorems for meromorphic self-maps of the projective space,
• Dynamics of automorphisms of compact complex surfaces,
• Bifurcation currents and equidistribution in parameter space,
• Entropy for hyperbolic Riemann surface laminations I,
• Entropy for hyperbolic Riemann surface laminations II,
• Intersection theory for ergodic solenoids,
• Invariants of four-manifolds with flows via cohomological field theory,
• Color Plates,
• Two papers which changed my life: Milnor's seminal work on at manifolds and bundles,
• Milnor's problem on the growth of groups and its consequences,
• Contributors,
• Index,