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Devaney R.L., Keen L. — Chaos and Fractals: The Mathematics Behind the Computer Graphics
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Название: Chaos and Fractals: The Mathematics Behind the Computer GraphicsАвторы: Devaney R.L., Keen L. Аннотация: This volume contains the proceedings of a highly successful AMS Short Course on Chaos and Fractals, held during the AMS Centennial Celebration in Providence, Rhode Island in August 1988. Chaos and fractals have been the subject of great interest in recent years and have proven to be useful in a variety of areas of mathematics and the sciences. The purpose of the short course was to provide a solid introduction to the mathematics underlying the notions of chaos and fractals. The papers in this book range over such topics as dynamical systems theory, Julia sets, the Mandelbrot set, attractors, the Smale horseshoe, calculus on fractals, and applications to data compression. The authors represented here are some of the top experts in this field. Aimed at beginning graduate students, college and university mathematics instructors, and non-mathematics researchers, this book provides readable expositions of several exciting topics of contemporary research.
Язык: Рубрика: Математика /Математическая Физика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1989Количество страниц: 148Добавлена в каталог: 24.04.2005Операции: Положить на полку |
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Предметный указатель
"Hot fudge" 123 "Snowflake" 115 Abstract Mandelbrot set 100 Accessible boundary point 49 Accumulation set 69 Affine transformations 128 Arzela — Ascoli theorem 60 AT-quasi-self-similar 65 Attracting 63 64 66 72 Attracting cycle 79 Attracting fixed point 4 66 Attracting periodic point 63 Attracting set 39 Attractive basin 66 80 Attractive cycle 66 70 Attractor 38 131 Base of attraction 38 Basin boundary metamorphoses 52 Basin of attraction 42 Bifurcation 7 Bifurcation diagram 11 Bifurcation set 81 Birkhoff, G.D. 51 Blanchard, P. 65 77 Borel measure 138 Bounded density 113 Box dimension 111 Branner 58 Brolin, H. 77 Brooks, R. 77 Camacho 65 Cantor set 14 32 71 115 Caratheodory 49 Cartwright and Littlewood 52 Cayley, A. 77 Cellular 93 Center of hyperbolic component 86 Chaos 17 Chaotic behavior 57 58 Chaotic trajectory 42 Collage theorem 135 Comparable net measures 111 Completely invariant 60 61 62 63 70 Completely invariant components 70 Complex exponential 22 Computer graphics 141 Condensation set 133 134 Condensation transformation 134 Connected 73 Connectivity 70 72 Continued fractal 118 Continued fraction 118 Contraction 113 Contraction mappings 130 Contraction ratio 113 Contractivity factor 134 136 Cremer 68 Critical 63 Critical point 58 64 66 67 69 70 73 78 Critical value 58 78 Cross section 28 CYCLE 6 78 Degree 58 Degree (of a rational map) 58 Dendrite 70 93 Denjoy counterexample 122 density 112 113 Deterministic algorithm 132 Devaney 57 Diameter 109 Diffeomorphism 115 Diophantine 68 Domain of attraction 38 Douady Rabbit 95 Douady, A. 1 73 77 Douady, A. and Hubbard, J.H. 91 98 102 Douady, A., Hubbard, J.H. and Sullivan, D. 85 Dynamical plane 78 Dynamical system behaves chaotically 60 Dynamical systems 57 58 Dynamically defined foliation 66 Eigenvalue 63 78 Elton’s ergodic theorem 128 Equicontinuous 60 Equipotential 92 Eventually fixed 4 Eventually periodic 65 66 Eventually periodic domains 65 examples 69 Exceptional set 63 expanding 64 73 Expanding maps 64 External argument 93 External rays 93 Fatou, P. 60 65 68 77 79 80 Feigenbaum 10 Ferns 127 Filled-in Julia set 80 First return map 2 Fisher, Y. 77 78 82 Fixed point 4 28 Flexed image 122 Flexible 122 Flower Theorem 67 Foliation 66 67 Fractal 1 14 109 127 Fractal boundary 47 Fractal geometry 127 Fundamental theorem of calculus 121 Generate 114 Golden mean 118 Grand orbit equivalent 66 Grand orbit relation 67 Graphical analysis 4 graphs 118 Green’s function 88 Guckenheimer’s example 62 70 Hausdorff dimension 109 110 Hausdorff distance 129 Hausdorff measure 73 109 110 111 Hausdorff metric 114 Hausdorff outer measure 110 Herman 65 69 Herman ring 69 70 73 Hoelder 120 Holmes 57 Homeomorphism 115 Homoclinic point 30 Homoclinic tangency 53 Horseshoe map 31 Hubbard, J.H. 1 77 82 Hutchinson metric 138 Hyperbolic 29 Hyperbolic component 83 Hyperbolicity conjecture 83 IFS 131 IFS code 132 Immediate attractive basin 66 67 Indifferent cycle 79 Infinitely connected 71 Internal argument 84 Invariant 113 122 Invariant foliation 69 Invariant measure 139 Iterated function system 131 Iteration 2 Itinerary 15 Julia set 1 18 60 61 62 64 65 70 71 80 Julia, G. 60 65 68 77 80 K-quasi-isometry 65 Koch curve 115 Lambda lemma 30 Lavaurs algorithm 99 Lebesgue density theorem 112 Lebesgue measure 110 Limb of internal argument p/q 84 Linearization 29 Lipschitz 115 Locally connected 94 97 Locally finite 111 Locally positive 111 Logistic equation 3 Lowest terms 58 Loxodromic Mapping Conjecture 123 Lyapunov exponent 41 Mandelbrot 1 77 82 108 Mandelbrot set 75 81 Matelski, P. 77 Mather, J. 52 Melnikov’s method 34 Milnor, J. 83 98 Minimal 122 Misiurewicz point 93 Montel’s theorem 60 61 62 63 102 Morse — Sard theorem 120 121 Multiplier 78 Net 112 Net measure 112 Neutral 63 64 Neutral cycle 79 Neutral periodic cycle 68 Newton’s method 58 Norm 109 normal 60 Normal family 60 62 101 Orbit 2 59 78 Parabolic 72 Parabolic cycle 67 70 Parabolic periodic cycle 67 Parameter plane 78 Parameters 58 Peano curve 115 Peitgen, H.-O. 78 Period q-doubling bifurcation 84 Period-doubling bifurcation 8 84 Period-p periodic cycle 63 Periodic 66 Periodic cycle 66 68 Periodic orbit 6 28 78 Periodic point 63 Phase-space 28 Poincare 122 Poincare linearization 63 Poincare map 2 Poincare metric 59 POINTS 63 Polynomial-like mappings 103 Post-critical set 59 68 73 Preperiodic orbit 78 Principal vein 93 Quadratic maps 57 Quasi-arc 117 Quasi-circle 117 Quasi-isometries 109 Random iteration algorithm 132 Rational map 57 58 59 Repelling 63 Repelling cycle 79 Repelling fixed point 4 Repelling periodic 64 Repelling periodic points 64 Richter, P. 78 Riemann mapping theorem 59 Rigid 113 Root of hyperbolic component 86 Rotation number 51 S-dimensional density 113 S-measure 110 S-set 111 Saddle node bifurcation 7 Saddle point 29 Sarkovskii’s theorem 19 Schroeder 64 Schwarz lemma 59 64 Seifert conjecture 123 Self-similar 65 113 Sensitive dependence 17 62 Sensitive dependence on initial conditions 33 Shift automorphism 14 Shishikura 65 66 73 Siegel disk 67 70 Siegel, C. 65 68 77 Sierpinski triangle 131 Similarity dimension 115 Similitude 115 Simple saddle-node bifurcation 23 Simply connected 72 Sink 4 29 Smale — Birkhoff homoclinic theorem 34 Source 4 29 Stable 30 62 64 Stable domains 66 Stable manifold 30 47 Stable point 60 Stable set 71 80 State-space 28 Strange attracting set 39 Strange Attractor 38 Structural stability 33 Subharmonic 28 Subshift of finite type 22 Sullivan, D. 65 66 77 Super-attracting 63 64 66 Super-attracting periodic points 64 Super-attracting stable domain 70 Super-attractive cycle 66 70 Super-attractive periodic point 66 Superattracting cycle 79 Symbolic dynamics 12 33 Tan Lei 102 Topological conjugacy 33 Topological dimension 109 Topologically transitive 17 Uniformization theorem 59 66 67 Unstable 64 Unstable manifold 30 47 Unstable point 62 Unstable set 60 Unstable subspaces 30 Wandering 65 Weierstrass functions 120 Whitney counterexample 121 Whitney extension theorem 120 Yorke 57
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