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

• Autore: Bonifant Araceli
• Pubblicazione: Princeton, New Jersey ; ; Oxfordshire, England : , : Princeton University Press, , 2014; ©2014
• Edizione: Course Book
• Descrizione fisica: 1 online resource (824 p.)
• Disciplina: 515.9
• Soggetto topico: Functions of complex variables; Differentiable dynamical systems
• Soggetto non controllato: John Milnor; Jordan curves; Julia sets; K-theory; M. Hakim; Maldelbrot set; Milnor's conjecture; Sierpinski carpets; Sierpinski gaskets; Thurston Rigidity Theorem; William Thurston; antiholomorphic quadratic polynomials; antiholomorphic unicritical polynomials; arithmetics; asymptotic behavior; automorphisms; biholomorphisms; combinatorial group theory; complex manifolds; complex polynomials; conformal distortion; conjugacy; connectedness loci; critical objects; critical point; critically finite case; decomposition; differential geometry; differential topology; dynamical cores; dynamical derivatives; dynamical scales; dynamical systems; dynamics; eigenvalues; entropy theory; entropy; escape regions; expanding critical orbits; external rays; geometrically finite rational maps; global meromorphic maps; holomorphic dynamics studies; holomorphic dynamics; holomorphic germs; holomorphic maps; hyperbolic distortion; hyperbolic geometry; hyperbolicity; identity germ; implosions; index theorems; infinitely renormalizable quadratic polynomials; integral closure; interval dynamics; irreducibility; kneading sequences; laminations; leading monomial vector; leading monomials; limiting behavior; local connectivity; local dynamics; mathematics; mating; metric stability; monotonicity; multicorn; non-locally connected Julia sets; one-dimensional maps; periodic critical orbit; periodic objects; periodic orbits; perturbations; polynomials; postcritically finite maps; projective space; pushforwards; quadratic differentials; quadratic dynatomic curves; quadratic polynomials; random walks; rational maps; renormalization theory; resurgence theory; rigidity; robustness; singularly perturbed rational maps; smoothness; spherical geometry; summability condition; summable critical points; topological entropy; topological polynomials; topological space; transversality theory; tricorn; unbounded hyperbolic components; unicritical polynomial maps; unimodal interval map; unmating
• Altri autori: BonifantAraceli LyubichMikhail SutherlandScott
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references at the end of each chapters and index.
• Nota di contenuto: 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
• Sommario/riassunto: 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.
• Titolo autorizzato: Frontiers in complex dynamics
• ISBN: 1-4008-5139-4; 1-4008-5131-9
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910789017803321
• Lo trovi qui: Univ. Federico II
• Serie: Princeton Mathematical Series