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Falconer K. — Fractal Geometry: Mathematical Foundations and Applications
Falconer K. — Fractal Geometry: Mathematical Foundations and Applications



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Название: Fractal Geometry: Mathematical Foundations and Applications

Автор: Falconer K.

Аннотация:

Since its original publication in 1990, Kenneth Falconer's Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals. It introduces the general mathematical theory and applications of fractals in a way that is accessible to students from a wide range of disciplines. This new edition has been extensively revised and updated. It features much new material, many additional exercises, notes and references, and an extended bibliography that reflects the development of the subject since the first edition.
* Provides a comprehensive and accessible introduction to the mathematical theory and applications of fractals.
* Each topic is carefully explained and illustrated by examples and figures.
* Includes all necessary mathematical background material.
* Includes notes and references to enable the reader to pursue individual topics.
* Features a wide selection of exercises, enabling the reader to develop their understanding of the theory.
* Supported by a Web site featuring solutions to exercises, and additional material for students and lecturers.
Fractal Geometry: Mathematical Foundations and Applications is aimed at undergraduate and graduate students studying courses in fractal geometry. The book also provides an excellent source of reference for researchers who encounter fractals in mathematics, physics, engineering, and the applied sciences.


Язык: en

Рубрика: Математика/Геометрия и топология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: second edition

Год издания: 2003

Количество страниц: 366

Добавлена в каталог: 14.11.2004

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