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| Авторизация |
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| Falconer K. — Fractal Geometry: Mathematical Foundations and Applications |
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| Предметный указатель |
Quasi-circle(s) 231 235—237
r-mesh cube 42 278
Radio antennas 309—311
Rainfall distribution 277
Random Cantor set 245 246—250 256
Random fractal(s) 244—256
Random function 259 260 270
Random mid-point displacement method 260
Random process 259
Random variable 20
Random variable, independence of 20—21
Random variable, simple 21
Random von Koch curve xxii xxiii 245 251 256
Random walk 258—259
Range, maximum 160
Ratio of contraction 128
Rational function 238
Rectifiable curve 81—84 181—182
Rectifiable curve, tangent 85—86
Reflection 8
Regular point 78
Regular set 78 80—89 93—94
Regular set, examples 81
Regular set, tangent 86—87
Removable set 179—181
Repeller 187—189 215
Repelling point 216 233
Repelling point, closure of 221
Reservoir level variations 160
Residence measure 208—209 277 283
Restriction of a measure 14
Rigid motion 8 109 111
Ring(s) of fractional dimension 182—184
Roessler band 204
Rotation 8
S-set 32 69 76
s-set, 0-set 77
s-set, 1-set 80—84 86—87 93—94
s-set, tangent to 84—88
Sample function 259 262 265
Sample space 18
Scalar multiple 4
Scaling property 29
Sections, parallel 105
Sector, double 85
Self-affme curve 166—169 312
Self-affme curve, construction of 166 167
Self-affme set 106—107 139—145
Self-affme set, as attractor 139 140 142 144 146
Self-affme set, construction of 107 142
Self-similar fractal with two different similarity ratios xxi
Self-similar measure 280 286 294
Self-similar measure, construction of 278 279
Self-similar measure, multifractal spectrum 288 293—296
Self-similar multifractals xxiv 286—296
Self-similar set xxiv 128—135
Self-similar set, similarity dimension xxiv (see also “Middle third Cantor set” “Sierpinski “von
Self-similarity xxii
Sensitive dependence on initial conditions 187 194 222
Set theory 3—6
Share prices 160 258 277 311—315
Siegel disc 232
Sierpinski dipole 310—311
Sierpinski gasket or triangle x xx 129 132 256
Similarity 7 8 29 111 128
Similarity dimension xxiv
Simple closed curve 230 235
Simple function 16
Simple random variable 21
Simulation 299
Singular value function 143
Singular value(s) 142
Singularity set 306
Singularity spectrum 284
Small divisor theory 205—208
Smooth manifold 41
Smooth set 32
Snowflake curve xix
Solenoid 98—201 200
Solid square, dimension print 56
Solution curves 201
Stability 41 48
Stability, countable 32 41 55
Stable point 191
Stable process 271—273 275
Stable set 216
| Stable symmetric process 272 273
Stationary increments 259 267 271
Statistically self-affine set 262 268 311
Statistically self-similar set 244 246 251 262 268
Stock market prices 160 258 277 311—315
Strange Attractor 186 205
Stretching and folding or cutting transformations 193—197 210
Strong Law of Large Numbers 24 152
Subgroup 182 183
Submanifold 29 48
Submultiplicative sequence 143
Subring 183—184
Subring, examples 183
Subset of finite measure 68—70
Sundial, digital 96—97
Superattractive point 238
Support of a measure 12
Supremum 5
Surface, convex 182
Surjection 7
Symbolic dynamics 189 212
Tangent xxv-xxvi 84—89
Tangent measure 89
Tangent plane 182
Tendril 232
Tends to 8
Tends to infinity 9
Tent map 188-189
Tent map repeller 188 189 190
Thermal convection 202
Topological dimension xxv
Torus 198—201
Totally disconnected set(s) 6 33 81 84 136 228 255
Trading time 312
Trail 258 262 264
Trajectories 201—202
Transformation(s) 6 7—8
Transformation(s), effects on a set 7
Transformation(s), group of 110 111
Transformation(s), linear 8
Transformation(s), stretching and folding or cutting 193—198 210
Translations 7—8
Tree antenna 310 311
Trial 18
Turbulence 307—309
Turbulence, fractally homogeneous 309
Turbulence, homogeneous 308
Turbulence, isotropic 307
Turbulent flow 307
Twist map 207
Ubiquity theorem 118
Uncountable set 5
Uniform Cantor set 63—64 103
Uniform convergence 10
Uniform distribution 23
Union of sets 4
Unstable point 191
Upper box(-counting) dimension 41
Upper coarse multifractal spectrum 280
Upper density of s-set 77
Upper limit 9
Variance 22
Vector sum of sets 4
Viscous fingering 277 300 304—305
Vitushkin's conjecture 179—181
Volume 14 45—46
Volume, scaling of 29
von Koch curve xviii—xx xix
von Koch curve, as self-similar set 123 129
von Koch curve, construction of xix 127—128
von Koch curve, dimension of xxiii
von Koch curve, features xx 35 123
von Koch curve, modified 132 133—134
von Koch curve, random xxii xxiii 245 251 256
von Koch dipole 310
von Koch snowflake xix
Vortex tubes 309
Weak solution 307
Weather prediction 204
Weierstrass function xxiii 160 162—166
Weierstrass function, random 270
Wiener process 258 259
“Cantor product” 99 100 102 103
“Cantor target” 103—104 104
“Dust-like” set 110
“Nearest point mapping” 181 182
“Venetian blind” construction, iterated 95—96 180
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