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



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Autore: Bonifant Araceli Visualizza persona
Titolo: Frontiers in complex dynamics : in celebration of John Milnor's 80th birthday / / edited by Araceli Bonifant, Mikhail Lyubich, and Scott Sutherland Visualizza cluster
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  Visualizza cluster
ISBN: 1-4008-5139-4
1-4008-5131-9
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910789017803321
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Serie: Princeton Mathematical Series