LEADER 04948nam 2200637 a 450 001 9910810237003321 005 20200520144314.0 010 $a1-281-92469-5 010 $a9786611924690 010 $a981-277-335-5 035 $a(CKB)1000000000402774 035 $a(EBL)1681239 035 $a(OCoLC)879025049 035 $a(SSID)ssj0000265242 035 $a(PQKBManifestationID)11218023 035 $a(PQKBTitleCode)TC0000265242 035 $a(PQKBWorkID)10294111 035 $a(PQKB)10999397 035 $a(MiAaPQ)EBC1681239 035 $a(WSP)00006136 035 $a(Au-PeEL)EBL1681239 035 $a(CaPaEBR)ebr10201465 035 $a(CaONFJC)MIL192469 035 $a(EXLCZ)991000000000402774 100 $a20060720d2006 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe universal mandelbrot set $ebeginning of the story /$fV. Dolotin, A. Morozov 205 $a1st ed. 210 $aHackensack, NJ $cWorld Scientiific Pub.$dc2006 215 $a1 online resource (176 p.) 300 $aDescription based upon print version of record. 311 $a981-256-837-9 320 $aIncludes bibliographical references (p. 161-162). 327 $aContents ; Preface ; 1. Introduction ; 2. Notions and notation ; 2.1 Objects associated with the space X ; 2.2 Objects associated with the space M ; 2.3 Combinatorial objects ; 2.4 Relations between the notions ; 3. Summary ; 3.1 Orbits and grand orbits ; 3.2 Mandelbrot sets 327 $a3.2.1 Forest structure 3.2.2 Relation to resultants and discriminants ; 3.2.3 Relation to stability domains ; 3.2.4 Critical points and locations of elementary domains ; 3.2.5 Perturbation theory and approximate self-similarity of Mandelbrot set ; 3.2.6 Trails in the forest 327 $a3.3 Sheaf of Julia sets over moduli space 4. Fragments of theory ; 4.1 Orbits and reduction theory of iterated maps ; 4.2 Bifurcations and discriminants: from real to complex ; 4.3 Discriminants and resultants for iterated maps ; 4.4 Period-doubling and beyond 327 $a4.5 Stability and Mandelbrot set 4.6 Towards the theory of Julia sets ; 4.6.1 Grand orbits and algebraic Julia sets ; 4.6.2 From algebraic to ordinary Julia set ; 4.6.3 Bifurcations of Julia set ; 4.7 On discriminant analysis for grand orbits 327 $a4.7.2 Irreducible constituents of discriminants and resultants 4.7.6 Summary ; 4.7.7 On interpretation of wntk ; 4.8 Combinatorics of discriminants and resultants ; 4.9 Shapes of Julia and Mandelbrot sets ; 4.9.1 Generalities 327 $a4.9.2 Exact statements about 1-parametric families of polynomials of power-d 330 $a This book is devoted to the structure of the Mandelbrot set - a remarkable and important feature of modern theoretical physics, related to chaos and fractals and simultaneously to analytical functions, Riemann surfaces, phase transitions and string theory. The Mandelbrot set is one of the bridges connecting the world of chaos and order. The authors restrict consideration to discrete dynamics of a single variable. This restriction preserves the most essential properties of the subject, but drastically simplifies computer simulations and the mathematical formalism. The coverage 606 $aMandelbrot sets 615 0$aMandelbrot sets. 676 $a514/.742 700 $aDolotin$b V$g(Valerii Valerevich)$01721103 701 $aMorozov$b A. D$g(Albert Dmitrievich),$f1944-$028597 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910810237003321 996 $aThe universal mandelbrot set$94120324 997 $aUNINA