04990nam 2200637 a 450 991045846230332120200520144314.01-281-92469-59786611924690981-277-335-5(CKB)1000000000402774(EBL)1681239(OCoLC)879025049(SSID)ssj0000265242(PQKBManifestationID)11218023(PQKBTitleCode)TC0000265242(PQKBWorkID)10294111(PQKB)10999397(MiAaPQ)EBC1681239(WSP)00006136(Au-PeEL)EBL1681239(CaPaEBR)ebr10201465(CaONFJC)MIL192469(EXLCZ)99100000000040277420060720d2006 uy 0engur|n|---|||||txtccrThe universal mandelbrot set[electronic resource] beginning of the story /V. Dolotin, A. MorozovHackensack, NJ World Scientiific Pub.c20061 online resource (176 p.)Description based upon print version of record.981-256-837-9 Includes bibliographical references (p. 161-162).Contents ; 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 sets3.2.1 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 forest3.3 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 beyond4.5 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 orbits4.7.2 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 Generalities4.9.2 Exact statements about 1-parametric families of polynomials of power-d 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 <i>discrete</i> dynamics <i>of a single variable</i>. This restriction preserves the most essential properties of the subject, but drastically simplifies computer simulations and the mathematical formalism. The coverage Mandelbrot setsElectronic books.Mandelbrot sets.514/.742Dolotin V(Valeriĭ Valerʹevich)934539Morozov A. D(Alʹbert Dmitrievich),1944-28597MiAaPQMiAaPQMiAaPQBOOK9910458462303321The universal mandelbrot set2104442UNINA