√лавна€    Ex Libris     ниги    ∆урналы    —татьи    —ерии     аталог    Wanted    «агрузка    ’удЋит    —правка    ѕоиск по индексам    ѕоиск    ‘орум   
blank
јвторизаци€

       
blank
ѕоиск по указател€м

blank
blank
blank
 расота
blank
Falconer K. Ч Fractal geometry: mathematical foundations and applications
Falconer K. Ч Fractal geometry: mathematical foundations and applications

„итать книгу
бесплатно

—качать книгу с нашего сайта нельз€

ќбсудите книгу на научном форуме



Ќашли опечатку?
¬ыделите ее мышкой и нажмите Ctrl+Enter


Ќазвание: Fractal geometry: mathematical foundations and applications

јвтор: Falconer K.

јннотаци€:

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

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

»здание: 2

√од издани€: 2003

 оличество страниц: 337

ƒобавлена в каталог: 12.12.2013

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
blank
ѕредметный указатель
'Cantor product'      99 100 102 103
'Cantor target'      103Ч104 704
'Dust-like' set      110
'Nearest point mapping'      181 182
'Venetian blind' construction, iterated      95Ч96 96 180
($\alpha$-)well approximable number(s)      155 155Ч157 205 207
(delta-)/($\delta$-)cover      27 28 30 36
(delta-)/($\delta$-)neighbourhood      4 45 112 124
(delta-)/($\delta$-)parallel body      4
(s-)capacity      72
(s-)energy      70
(s-)potential      70
(sigma-)/$\sigma$-finite measure      95
Affine transformation      8 139
Affinity      7 8
Almost all      16 85
Almost everywhere      16
Almost surely      19
Analytic function      138 180 215
Antennas      309Ч311 310
arc, dimension print      56
Area      14
Area, scaling of      29
Arnold's cat map      213
Astronomical evidence, for small divisors      208
Attractive orbit      228
Attractive point      216 222
Attractor      123 123Ч128 127 139 140 187
Attractor in continuous dynamical system      201Ч205
Attractor in discrete dynamical system      187 189 192 194
Autocorrelation      169Ч173 268
Autocorrelation function      170
Average      21
Avogadro's number      258
Baker's transformation      193 193Ч194 194 210 211
Ball      4
Banach's contraction mapping theorem      124 125
Basic interval      35 62 127 152
Basin of attraction      187 201 222 238Ч241
Besicovitch construction      178 179
Besicovitch set      179
Bi-Lipschitz equivalence      236
Bi-lipschitz function      8 103
Bi-Lipschitz transformation      32 33 41
Bifurcation diagram      192
Bijection      7 236
Binary interval      16 36
Borel set(s)      6
Borel set(s) and duality      178
Borel set(s) and intersections      111
Borel set(s) and products      100 101 105 106
Borel set(s) and projections      90 93
Borel set(s) and subrings      183Ч184
Borel set(s) and subsets of finite measure      68 69 70
Borel set(s), measure on      11Ч12
Boundary      5 6
Bounded set      5 114
Bounded variation      86
Box counting      283 298
Box(-counting) dimension      41 41Ч47 43 44
Box(-counting) dimension and growth      299Ч300
Box(-counting) dimension and Hausdorff dimension      46 60
Box(-counting) dimension, Brownian motion      263 265
Box(-counting) dimension, fractional Brownian motion      268
Box(-counting) dimension, fractional Brownian surface      273
Box(-counting) dimension, Levy stable process      272
Box(-counting) dimension, limitations      48
Box(-counting) dimension, modified      49 49Ч50
Box(-counting) dimension, problems      48Ч49
Box(-counting) dimension, properties      47Ч48
Box(-counting) dimension, ways of finding      44 47
Branch      223
Branching process theory      250
Brownian graph      266
Brownian motion      37 258Ч267 259 261 298 299 311Ч315
Brownian motion, Fourier series representation      260
Brownian motion, fractional      173 267 267Ч271 269 275
Brownian motion, index-$\alpha$ fractional      267 261Ч211 269 311
Brownian motion, multifractional      271
Brownian motion, n-dimensional      260
Brownian sample function      259 261 262
Brownian sample function, graph      265Ч266
Brownian sample function, index-$\alpha$ fractional      273
Brownian sample function, multiple points      265
Brownian surface, fractional      273Ч275
Brownian trail(s)      258 261 262 264Ч265
Cantor dust      xx xxi 94 126
Cantor dust, calculation of Hausdorff dimension      34
Cantor dust, construction of      xxi 34
Cantor set      see also "Middle third Cantor set"
Cantor set as attractor      189 192 194
Cantor set, construction of      61Ч62
Cantor set, dimension of      xxiii 34Ч35 47
Cantor set, middle $\lambda$      64
Cantor set, middle third      xvii xviii 34Ч35 47 60 61 63Ч64 87 99 100 112 123Ч124 127 129 188 189
Cantor set, non-linear      136Ч137 154
Cantor set, random      245Ч246 246Ч250 256
Cantor set, uniform      63Ч64 64 103 141
Capacity dimension      41
Cartesian product      4 87 99 100
Cat map      213
Cauchy sequence      125
Central limit theorem      24 259
Chaos      189
Chaotic attractor      189 192
Chaotic repeller      189
Characteristic function      271
Choleski decomposition      270
Circle perimeter, dimension print      56
Class $\mathcal{C}^{s}$      113 113Ч118 157
Class $\mathcal{C}^{s}$, member      113
Closed ball      4 66
Closed interval      4
Closed loop, as attractor      201
Closed set      5 114 201
Closure of set      6
Cloud boundaries      244 298
Coarse multifractal spectrum      278Ч279
Coarse multifractal spectrum, lower      280
Coarse multifractal spectrum, upper      280
Coastline(s)      54 244 298
Codomain      7
Collage theorem      145
Compact set      6 48
Complement of a set      4
Complete metric      125
Complex dynamics      216
Composition of functions      7
Computer drawings      127Ч128 128 145Ч148 196 227 232 233 234 239 240 244 260 269 270Ч271 275
Conditional expectation      22
Conditional probability      19
Conformal mapping      138Ч139 180 241
Congruence(s)      7 112
Congruence(s), direct      8
Conjugacy      223
Connected component      6
Connected set      6
Content, Minkowski      45
Content, s-dimensional      45
Continued fraction expansion      153
Continued fraction(s)      153Ч154
Continued fraction(s), examples      153
Continuity equation      203
Continuous dynamical systems      201Ч205
Continuous function      10
Continuously differentiable function      10
contours      275
Contracting similarity      123
Contraction      123
Contraction mapping theorem      124 125
Convergence      8
Convergence of sequence      5
Convergence, pointwise      10
Convergence, uniform      10 17
Convex function      181 181Ч182 287
Convex surface      182
Convolution theorem      73 172
Coordinate cube      4
Copper sulphate, electrolysis of      300Ч301 302Ч304
Correlation      169Ч173 268 311
Countable set      4 32 41
Countable stability of dimension print      55
Countable stability of Hausdorff dimension      32 41
Counting measure      13
Covariance matrix      270
Cover of a set      27 28 30 35Ч36 see
Covering lemma      66Ч67
critical exponent      54
Critical point      227 228
Cross section      202
cube      4 42
Cubic polynomial, Newton's method for      239Ч241 240
Curve      53 81
Curve, fractal      133Ч134
Curve, Jordan      53 81
Curve, rectifiable      81 81Ч84 85Ч86 181Ч182
Curve-free set      81 83 83Ч84
Curve-like set      81 82Ч83 83Ч84
Darcy's law      305
Data compression      145Ч148
Decomposition of 1-sets      80Ч81 81
Dendrite      232
Dense set      6
density      76 76Ч80 84 88 152
Density function      306
Density, lower      77 84
Density, upper      77
Derivative      10
Diameter of subset      5 27
Difference of sets      4
Differentiability      10 137Ч138 160 182
Differentiability, continuous      10
Diffusion equation      303
Diffusion limited aggregation (DLA) model      301Ч306 302 303
Digital sundial      96Ч97 97
DIMENSION      xxiiЧxxv xxiv
Dimension function      37
Dimension of ($\alpha$-)well approximable number      155
Dimension of a measure      288
Dimension of attractors and repellers      186Ч201
Dimension of Cantor set      xxiii
Dimension of graphs of functions      160Ч169 161
Dimension of intersections      109Ч118
Dimension of products      99Ч107
Dimension of projections      90Ч97
Dimension of random sets      246Ч251 259Ч275
Dimension of self-affine sets      106Ч107 139Ч144 166Ч169
Dimension of self-similar sets      xxiv 128Ч135
Dimension of von Koch curve      xxiii
Dimension print      54Ч57 55 56
Dimension print, disadvantages      55Ч56
Dimension print, examples      56
Dimension, alternative definitions      39Ч58
Dimension, approximations to      299 305
Dimension, box(-counting)      41 41Ч50 43 44 60 263 265 268 272 273 299Ч300
Dimension, calculation of      34Ч35 59Ч75 128Ч135
Dimension, capacity      41
Dimension, characterization of quasi-circles by      235Ч237
Dimension, divider      39 53Ч54
Dimension, entropy      41
Dimension, experimental estimation of      39Ч40 299Ч300
Dimension, finer definitions      36Ч37
Dimension, Fourier      74
Dimension, Hausdorff      xxiv 27 31 31Ч33 35Ч36 40 54 70 92
Dimension, Hausdorff dimension of a measure      209 288
Dimension, Hausdorff Ч Besicovitch      31
Dimension, information      41
Dimension, local      283
Dimension, lower box(-counting)      41 43
Dimension, metric      41
Dimension, Minkowski( Ч Bouligand)      46
Dimension, modified box-counting      49 49Ч50
Dimension, one-sided      54
Dimension, packing      50Ч53 51
Dimension, similarity      xxiv
Dimension, topological      xxv
Dimension, upper box(-counting)      41 43
Dimensionally homogeneous set      50
Diophantine approximation      153 154Ч157 205
Direct congruence      8
Dirichlet's theorem      154
Discrete dynamical system      186 186Ч201
Disjoint binary intervals      36
Disjoint collection of sets      4
Distance set      183
Distribution of digits      151Ч153
Distribution, Gaussian      23
Distribution, multidimensional normal      262
Distribution, normal      23 260
Distribution, uniform      23
Divider dimension      39 53Ч54
Domain      7
Double sector      85
Duality method      176Ч179 777
Dynamical systems      186Ч212
Dynamical systems, continuous      201Ч205
Dynamical systems, discrete      186 186Ч201
Dynamics, complex      216
Eddies      308
Egoroff's theorem      17 79
Electrical discharge in gas      305
Electrodynamics      310
Electrolysis      300Ч301 301 302Ч304
Electrostatic potential      70 305 306Ч307
entropy      209Ч211 210
Entropy dimension      41
Ergodic theory      128 209
Euclidean distance or metric      3
Euclidean space      3
Event      18
Event space      18
Event, independence of      20
Exchange rate variation      311 313
Expectation      21
Expectation equation      247 250
Expectation, conditional      22
Experiment (probabilistic)      18
Experimental approach to fractals      39Ч40 299Ч300
Exterior, of loop      223
Extinction probability      250
Fatou set      216 235
Feigenbaum constant      193
Figure of eight      223 228
Filled-in Julia set      215
finance      186 311Ч315
Fine (Hausdorff) multifractal spectrum      284
Fine multifractal analysis      277 283Ч286
First return map      202
Fixed point      125 186 216
Fluid dynamics      277 307Ч309
Forked lightning      298 300
Fourier dimension      74
Fourier series      206
Fourier transform      73 92
Fourier transform, methods using      73Ч74 112 171Ч173 260 271
Fractal curve      133Ч134 216
Fractal growth      300Ч306
Fractal interpolation      169 170
Fractal percolation      251Ч255
Fractal, definition      xxii xxv
1 2 3
blank
–еклама
blank
blank
HR
@Mail.ru
       © Ёлектронна€ библиотека попечительского совета мехмата ћ√”, 2004-2017
Ёлектронна€ библиотека мехмата ћ√” | Valid HTML 4.01! | Valid CSS! ќ проекте