Falconer K. — Fractal Geometry. Mathematical Foundations and applications :: Электронная библиотека попечительского совета мехмата МГУ

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Falconer K. — Fractal Geometry. Mathematical Foundations and applications

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Название: Fractal Geometry. Mathematical Foundations and applications

Автор: Falconer K.

Аннотация:

An accessible introduction to fractals, useful as a text or reference. Part I is concerned with the general theory of fractals and their geometry, covering dimensions and their methods of calculation, plus the local form of fractals and their projections and intersections. Part II contains examples of fractals drawn from a wide variety of areas of mathematics and physics, including self-similar and self-affine sets, graphs of functions, examples from number theory and pure mathematics, dynamical systems, Julia sets, random fractals and some physical applications. Also contains many diagrams and illustrative examples, includes computer drawings of fractals, and shows how to produce further drawings for themselves.

Язык:

Рубрика: Математика/Геометрия и топология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1990

Количество страниц: 288

Добавлена в каталог: 14.11.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Open set      5
Open set condition      118 118—120 229
Orbit      170 197 209 212—215
Orthogonal projection      83—91
Packing dimension      47 47—49
Packing measure      47 47—49 81
Parseval's theorem      67
Partial quotients      140
Path      237
Percolation      231—236 233
Perfect set      202
Period doubling      174—176
Period-p point      170 197
Phase transition      235
Physical applications      xxi 263 265—277
Poincare — Bendixson theorem      184
Poisson's equation      273
Polynomial      197—217 219—222
Population dynamics      173 176
Porous flow      272
Potential theory      64—66 84 103 272—273
Power spectrum      156 156—158 247
Pre-fractal      115 116
Pre-image      6
Probability density function      21
Probability measure      17
Probability space      18
Probability theory      16—23
Product, cartesian      4 56 92 92—100
Projection      83—91
Projection at a point      91
Projection theorems      83—86
Quadratic functions      204—217 219—220
Quasi-circles      211 217 217—218
Random fractal      224—236
Random function      238
Random mid-point displacement      239
Random process      238
Random variable      19
Random variable, simple      20
Random walk      237—239
Range, maximum      146 146—147
Rational function      197 219
Rectifiable curve      74 74—78 166
Reflection      7
Regular point      70 73
Regular set      70 70—82 86—87 164
Removable set      164 164—165 169
Repeller      171 171—176 196 198 218
Repelling point      197
Rigid motion      7 101—104
Ring      167—168
Roessler band      187—188
Rotation      7
Sample function      238 238—253
Sample space      17
Scaling property      27
Section      97—98 250
Sector, double      77
Self-affine curve      153 —155
Self-affine set      99 100 126—132 127
Self-similar measure      255 261 263
Self-similar set      117 117—123 275
Sensitive dependence on initial conditions      171
Set theory      3—6
Siegel disc      215

Sierpinski gasket      xvi 120 236
Sigma-finite measure      87
Similarity      7 101—104 113 117
Simple function      15
Simulation      265—266
Singular value function      130
Singular values      129
Singularity set      272—273
Small divisors      188—191
Solenoid      182—184
Solution curves      184
Stability      37
Stability countable      37
Stable point      174
Stable process      248—250
Stable set      198
Stable symmetric process      249
Stationary increments      238 246 248
Statistically self-affine set      240 246 249
Statistically self-similar set      224—236 240 246 249
Stretching and folding or cutting transformations      177—181
Strong Law of Large Numbers      22 24 139
Subgroup      167 167—169
Submanifold      26 29 37 101 103
Submultiplicative sequence      130
Subring      167 167—169
Subset of finite measure      62—64
Superattractive point      197
Support of a measure      11
Supremum      4
Surface, convex      165 165—167
Surjection      6
Symbolic dynamics      173
Tangent      77 77—81
Tangent plane      165
Tends to      8
Tent map      172
Thermal convection      186
Torus      182—184
Totally disconnected      6 30 77 116 234
Trail      237
Trajectories      184
Transformation      6 7
Translations      7 101—104
Trial      17
Turbulence      273—277
Turbulence, fractally homogeneous      274—276
Turbulence, homogeneous      274
Twist map      190
Uncountable set      4
Uniform convergence      10 16
Uniform distribution      22
union      4
Unstable point      174
Variance      21
Vector sum      4
Virushkin's conjecture      164—165
Viscous fingering      271—272
Volume      13 26 42
von Koch curve      xiv —xvi 113 117
von Koch curve, modified      120—121
von Koch curve, random      xvii 224—225 230 235
Weak solutions      273 276
Weierstrass function      xvii 148—152 159—160
Weierstrass function, random      247
Wiener process      238

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