LEADER 09870nam 2201909 450 001 9910828074103321 005 20230803201813.0 010 $a1-4008-5139-4 010 $a1-4008-5131-9 024 7 $a10.1515/9781400851317 035 $a(CKB)3710000000088696 035 $a(EBL)1609165 035 $a(OCoLC)871190735 035 $a(SSID)ssj0001173343 035 $a(PQKBManifestationID)11748392 035 $a(PQKBTitleCode)TC0001173343 035 $a(PQKBWorkID)11102389 035 $a(PQKB)11157521 035 $a(MiAaPQ)EBC1609165 035 $a(StDuBDS)EDZ0001756471 035 $a(DE-B1597)453975 035 $a(OCoLC)979630037 035 $a(DE-B1597)9781400851317 035 $a(Au-PeEL)EBL1609165 035 $a(CaPaEBR)ebr10838551 035 $a(CaONFJC)MIL576904 035 $a(EXLCZ)993710000000088696 100 $a20140225h20142014 uy 0 101 0 $aeng 135 $aurnn#---|u||u 181 $ctxt 182 $cc 183 $acr 200 00$aFrontiers in complex dynamics $ein celebration of John Milnor's 80th birthday /$fedited by Araceli Bonifant, Mikhail Lyubich, and Scott Sutherland 205 $aCourse Book 210 1$aPrinceton, New Jersey ;$aOxfordshire, England :$cPrinceton University Press,$d2014. 210 4$d©2014 215 $a1 online resource (824 p.) 225 0 $aPrinceton Mathematical Series 300 $aDescription based upon print version of record. 311 0 $a0-691-15929-7 320 $aIncludes bibliographical references at the end of each chapters and index. 327 $tFront matter --$tContents --$tPreface --$tIntroduction --$tPart I. One Complex Variable --$tArithmetic of Unicritical Polynomial Maps /$rMilnor, John --$tLes racines des composantes hyperboliques de M sont des quarts d'entiers algébriques /$rBousch, Thierry --$tDynamical cores of topological polynomials /$rBlokh, Alexander / Oversteegen, Lex / Ptacek, Ross / Timorin, Vladlen --$tThe quadratic dynatomic curves are smooth and irreducible /$rBu, Xavier / Lei, Tan --$tMulticorns are not path connected /$rHubbard, John Hamal / Schleicher, Dierk --$tLeading monomials of escape regions /$rKiwi, Jan --$tLimiting behavior of Julia sets of singularly perturbed rational maps /$rDevaney, Robert L. --$tOn (non-)local connectivity of some Julia sets /$rDezotti, Alexandre / Roesch, Pascale --$tPerturbations of weakly expanding critical orbits /$rLevin, Genadi --$tUnmating of rational maps: Sufficient criteria and examples /$rMeyer, Daniel --$tA framework toward understanding the characterization of holomorphic dynamics /$rJiang, Yunping --$tPart II. One Real Variable --$tMetric stability for random walks (with applications in renormalization theory) /$rMoreira, Carlos Gustavo / Smania, Daniel --$tMilnor's conjecture on monotonicity of topological entropy: Results and questions /$rStrien, Sebastian van --$tEntropy in dimension one /$rThurston, William P. --$tPart III. Several Complex Variables --$tOn Écalle-Hakim's theorems in holomorphic dynamics /$rArizzi, Marco / Raissy, Jasmin --$tIndex theorems for meromorphic self-maps of the projective space /$rAbate, Marco --$tDynamics of automorphisms of compact complex surfaces /$rCantat, Serge --$tBifurcation currents and equidistribution in parameter space /$rDujardin, Romain --$tPart IV. Laminations and Foliations --$tEntropy for hyperbolic Riemann surface laminations I /$rDinh, Tien-Cuong / Nguyên, Viet-Anh / Sibony, Nessim --$tEntropy for hyperbolic Riemann surface laminations II /$rDinh, Tien-Cuong / Nguyên, Viet-Anh / Sibony, Nessim --$tIntersection theory for ergodic solenoids /$rMuñoz, Vicente / Pérez-Marco, Ricardo --$tInvariants of four-manifolds with flows via cohomological field theory /$rGarcía-Compeán, Hugo / Santos-Silva, Roberto / Verjovsky, Alberto --$tColor Plates --$tPart V. Geometry and Algebra --$tTwo papers which changed my life: Milnor's seminal work on at manifolds and bundles /$rGoldman, William M. --$tMilnor's problem on the growth of groups and its consequences /$rGrigorchuk, Rostislav --$tContributors --$tIndex 330 $aJohn Milnor, best known for his work in differential topology, K-theory, and dynamical systems, is one of only three mathematicians to have won the Fields medal, the Abel prize, and the Wolf prize, and is the only one to have received all three of the Leroy P. Steele prizes. In honor of his eightieth birthday, this book gathers together surveys and papers inspired by Milnor's work, from distinguished experts examining not only holomorphic dynamics in one and several variables, but also differential geometry, entropy theory, and combinatorial group theory. The book contains the last paper written by William Thurston, as well as a short paper by John Milnor himself. Introductory sections put the papers in mathematical and historical perspective, color figures are included, and an index facilitates browsing. This collection will be useful to students and researchers for decades to come. The contributors are Marco Abate, Marco Arizzi, Alexander Blokh, Thierry Bousch, Xavier Buff, Serge Cantat, Tao Chen, Robert Devaney, Alexandre Dezotti, Tien-Cuong Dinh, Romain Dujardin, Hugo García-Compeán, William Goldman, Rotislav Grigorchuk, John Hubbard, Yunping Jiang, Linda Keen, Jan Kiwi, Genadi Levin, Daniel Meyer, John Milnor, Carlos Moreira, Vincente Muñoz, Viet-Anh Nguyên, Lex Oversteegen, Ricardo Pérez-Marco, Ross Ptacek, Jasmin Raissy, Pascale Roesch, Roberto Santos-Silva, Dierk Schleicher, Nessim Sibony, Daniel Smania, Tan Lei, William Thurston, Vladlen Timorin, Sebastian van Strien, and Alberto Verjovsky. 410 0$aPrinceton Mathematical Series 606 $aFunctions of complex variables 606 $aDifferentiable dynamical systems 610 $aJohn Milnor. 610 $aJordan curves. 610 $aJulia sets. 610 $aK-theory. 610 $aM. Hakim. 610 $aMaldelbrot set. 610 $aMilnor's conjecture. 610 $aSierpinski carpets. 610 $aSierpinski gaskets. 610 $aThurston Rigidity Theorem. 610 $aWilliam Thurston. 610 $aantiholomorphic quadratic polynomials. 610 $aantiholomorphic unicritical polynomials. 610 $aarithmetics. 610 $aasymptotic behavior. 610 $aautomorphisms. 610 $abiholomorphisms. 610 $acombinatorial group theory. 610 $acomplex manifolds. 610 $acomplex polynomials. 610 $aconformal distortion. 610 $aconjugacy. 610 $aconnectedness loci. 610 $acritical objects. 610 $acritical point. 610 $acritically finite case. 610 $adecomposition. 610 $adifferential geometry. 610 $adifferential topology. 610 $adynamical cores. 610 $adynamical derivatives. 610 $adynamical scales. 610 $adynamical systems. 610 $adynamics. 610 $aeigenvalues. 610 $aentropy theory. 610 $aentropy. 610 $aescape regions. 610 $aexpanding critical orbits. 610 $aexternal rays. 610 $ageometrically finite rational maps. 610 $aglobal meromorphic maps. 610 $aholomorphic dynamics studies. 610 $aholomorphic dynamics. 610 $aholomorphic germs. 610 $aholomorphic maps. 610 $ahyperbolic distortion. 610 $ahyperbolic geometry. 610 $ahyperbolicity. 610 $aidentity germ. 610 $aimplosions. 610 $aindex theorems. 610 $ainfinitely renormalizable quadratic polynomials. 610 $aintegral closure. 610 $ainterval dynamics. 610 $airreducibility. 610 $akneading sequences. 610 $alaminations. 610 $aleading monomial vector. 610 $aleading monomials. 610 $alimiting behavior. 610 $alocal connectivity. 610 $alocal dynamics. 610 $amathematics. 610 $amating. 610 $ametric stability. 610 $amonotonicity. 610 $amulticorn. 610 $anon-locally connected Julia sets. 610 $aone-dimensional maps. 610 $aperiodic critical orbit. 610 $aperiodic objects. 610 $aperiodic orbits. 610 $aperturbations. 610 $apolynomials. 610 $apostcritically finite maps. 610 $aprojective space. 610 $apushforwards. 610 $aquadratic differentials. 610 $aquadratic dynatomic curves. 610 $aquadratic polynomials. 610 $arandom walks. 610 $arational maps. 610 $arenormalization theory. 610 $aresurgence theory. 610 $arigidity. 610 $arobustness. 610 $asingularly perturbed rational maps. 610 $asmoothness. 610 $aspherical geometry. 610 $asummability condition. 610 $asummable critical points. 610 $atopological entropy. 610 $atopological polynomials. 610 $atopological space. 610 $atransversality theory. 610 $atricorn. 610 $aunbounded hyperbolic components. 610 $aunicritical polynomial maps. 610 $aunimodal interval map. 610 $aunmating. 615 0$aFunctions of complex variables. 615 0$aDifferentiable dynamical systems. 676 $a515.9 700 $aBonifant$b Araceli$0524939 701 $aBonifant$b Araceli$0524939 701 $aLyubich$b Mikhail$0287153 701 $aSutherland$b Scott$01686685 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910828074103321 996 $aFrontiers in complex dynamics$94059647 997 $aUNINA