Devaney R.L., Keen L. — Chaos and Fractals: The Mathematics Behind the Computer Graphics :: Электронная библиотека попечительского совета мехмата МГУ

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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 Graphics

Авторы: 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: 1989

Количество страниц: 148

Добавлена в каталог: 24.04.2005

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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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