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Schroeder M.R. — Schroeder, Self Similarity: Chaos, Fractals, Power Laws
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Название: Schroeder, Self Similarity: Chaos, Fractals, Power LawsАвтор: Schroeder M.R. Аннотация: Readers of James Gleick's 1989 bestseller, Chaos, The Making of a New Science, will find the revolution predicted there in full swing in this advanced look at "self-similarity, ' ' one of chaos theory's most appealing applications. Self-similarity in computer graphics yields the awesome fractal mountain patterns that have made chaos a visible theory for many nonmathematicians. Readers with good command of calculus and some physics will appreciate how far chaos theory has penetrated theoretical physics, biology and the practice of research as described in puns, illustrations and puzzles by this 20th-century Lewis Carroll. Without those skills, however, readers may stand like Alice before a small door that opens on strange new wonders of the physical world, the extended horizons of number theory and advanced math recreation. Schroeder is a professor of physics at Goettingen University in Germany.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1991Количество страниц: 432Добавлена в каталог: 09.04.2008Операции: Положить на полку |
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Предметный указатель
Schwarzschild exponent 66 Schwarzschild radius 65 Schwarzschild, K. 65 Searby, G. [ASS 86] Self-affine 112 122 141 174 Self-affine distribution 188 190 Self-affine fractal 191 Self-affine function 209 Self-affinity 153 Self-generating sequence 264 Self-organization 357 Self-organized criticality 389 Self-similar agglomerate 218 Self-similar cascade 279 Self-similar data 116 Self-similar distribution 157 Self-similar lattice 362 Self-similar scaling 341 Self-similar sequence 386 Self-similar set 163 201 Self-similar tiling 13 14 Self-similar tree 37 119 Self-similar TV antenna 86 Self-similarity 31 39 47 59 122 153 190 211 237 255 260 272 276 278 307 310 330 333 346 356 357 363 367 383 385 389 Self-similarity in architecture 84 Semiconductor 34 123 Semitone 95 96 101 Sessler, G.M. [ASSW 66] [SASW [Ses Shannon, C.E. [Sha 51] [Sha 35 127 149 360 Shannon’s information capacity 128 Shannon’s information theory 151 Shannon’s outguessing machine 150 Sharkovskii, A.N. [Sha 64] Sharkovskii’s ordering 2 281 285 Shechtman, D. [SBGC 84] 302 Shenker, S.J. [She 82] 333 343 Shepard, R.N. [She 62] [She 95 Shephard, G.C. [GS 87] Shepherding moon 338 Shisha, O. [CS 88] 7 Short range law 306 Short-time spectral analysis 73 Shraiman, B.I. [HJKPS 86] Sidles, C. [AZL...89] Siebesma, A.P. [PS 86] Siebrasse, F.K. [SGS 74] Sierpinski gasket 2 17 388 Sierpinski point 24 25 Sierpinski, W. 17 Sigma sequence 283 288 Silver mean 49 51 92 316 327 Silver-mean slope 56 Simaika, Y.M. [HBS 65] Similarity 61 79 Similarity dimension 216 391 Similarity factor 93 167 Similarity principle 67 Similarity solution 69 Simon, B. [AS 81] Sinc function 98 Singer, D. [Sin 78] Sir Pinski’s game 20 Site percolation 30 Size scale 380 Slater, P. [Sla 60] Slaved oscillator 338 Sloane, N.J.A. [Slo 73] [HS Smale, S. [Sma 67] Smale’s horseshoe map 253 Smith, P.W. [BS 84] Smoluchowski, M. 140 Solar system 316 Sound absorption 69 Sound decay 125 Sound diffraction 77 Sound diffusion 125 Sound intensity 34 Sound reproduction 79 Sound transmission 72 Sound-scattering surface 79 Space normalization 368 Space time 41 Spanning cluster 368 Spatial chaos 319 Spatial correlation 249 Spatial frequency 235 Special relativity 4 Specific heat 40 353 Spectral dimension 43 Spectral exponent 130 137 Speech signal 127 Speed 34 Spin 320 361 Spin domain 379 Spin glass 302 322 366 Spin interaction 362 Spin pattern 324 329 Square lattice 30 55 312 348 365 Sreenivasan, K.R. [MS 87] St. Petersburg paradox 148 Stability 316 Staircase 169 Staircase distributions 171 Staircase function 57 Stanley, H.E. [SO 85] [MSCW [MCSW [SM [Sta 198 State diagram 358 Stationary distribution 242 Stationary source 359 Statistical analysis 71 Statistical artifact 131 Statistical fluctuation 72 Statistical mechanics 206 222 Statistical misdemeanor 147 Statistical self-similarity 152 Statistically self-similar process 112 141 Statistically similar 141 Stauffer, D. [Sta 85] [ASS 345 354 367 Stavans, J. [JKLPS 85] Stein, M.L. [MSS 73] Stein, P.R. [MSS 73] Steinhardt, P.J. [LS 84] 313 Stereophonic sound 79 Stevens, S.S. [Ste 69] 70 Stevenson, J.M. [AZL...89] Stock market 127 128 Stokes, J.P. [SWGDRCL 86] Strange Attractor 27 28 201 206 207 253 Strauss, E. 3 Strong nuclear interaction 106 Strube, H.W. 12 315 391 Subjective brightness 71 95 Subjective loudness 34 Subjective rating 74 Subjective variable 71 Subset of multifractal 193 Sundar Raj, A.P. [KS 87] Sundial 181 Sunlight-blocking dust 105 Supercomputer 167 258 363 Superconductivity 43 334 Supercritical liquid 361 Superfast algorithm 258 Superionic conductor 172 Superlattice 368 Supersite 367 Superstable fixed point 269 Superstable orbit 269 273 277 285 294 341 Support interval 202 Support of a fractal set 245 Support of a multifractal 192 Support of the attractor 201 Supporting fractal 201 Surface dimension 136 Surface fractal 234 Surface reaction 143 Surface tension 200 Sutner, K. [Sut 89] Suwa, N. [ST 71] Symbolic dynamics 166 267 277 284 285 324 342 Symbolic sequence 279 Synchronization of two oscillators 171 Synchronization problem 306 Szell, G. 74 Sztajno, M. [HLSTLW 86] Taccetti, N. [BBFT 89] Takahashi, T. [ST 73] Tang, C. [BTW 87] [BTW [TB 389 Tangent bifurcation 289 290 Tempered scale 101 Tent map 165 288 292 Ternary number system 162 163 169 Test of relativity 114 Thermal noise 121 Thermal velocity 144 Thermodynamics 206 Thomae, S. [GT 77] [PTT 275 342 Thomas, J. [TKFFHKMM 89] Thompson, D’A.W. [Tho 61] Thompson, D’Arcy 63 Three-body encounter 25 Three-body problem 338 Thrice-iterated quadratic map 289 291 Thue, A. [Thu 06] 264 Tidal force 338 Time plane 133 Time series 223 Time vector 133 Time-limited data 131 Toffoli, T. [TM 87] Tomographic imaging 134 Toner, J. [OT 86] Topological dimension 153 Totally disconnected set 162 Toulouse, G. [RTV 86] Tower of Hanoi problem 238 Traditional scale 102 Transcendental number 242 Transfer matrix 77 Transfinite number 17 Transition probability 150 Transition to chaos 342 Transitivity 71 Translational symmetry 302 Trapped iterate 290 Tree design 117 Tressor, C. [PTT 87] 342 Triadic Cantor set 31 Triangular lattice 353 365 367 Tritave 102 True on all scales 33 63 107 112 162 Truemper, J. [HSLSTLW 86] Turbulence 167 195 320 Turtle algorithm 259 Turtle interpretation 260 Twelvefold symmetry 318 Twin dragon 47 50 Two-dimensional Fourier transform 133 Two-dimensional quasicrystal 313 Two-nation boundary 38 Ulam, S. [Ula 74] 371 Ulrich, S. [Ulr 72] Ultrametric space 88 Umberger, D.K. [EU 86] Uncertainty 71 113 Uncertainty principle 112 Uncertainty relation 114 Uncountable set 16 161 242 Undecidability in number theory 177 Unimodal map 279 283 Unimodular fractions 335 Universal function 350 Universal mechanism 115 Universal order 285 Universality 332 350 352 361 390 Universe 98 115 139 152 155 Unpredictability 167 245 294 Unstable equilibrium 256 VACUUM 114 Vacuum fluctuation 114 Valery, P. 61 Van der Pol, B. 109 Vascular system 119 Velocity profile 159 Verhulst equation 269 Verhulst, P.-F. [Ver 1845] 269 Vibrating fractal 44 Vichniac, G. [Vic 84] [Vic Vilenkin, A. [Vil 87] Virasoro, M.A. [RTV 86] Virial theorem 67 113 Viscous boundary layer 70 Viscous fingering 199 219 Visual perception 340 Vocal tract 44 von Boehm, J. [BB 79] von der Poorten, A. [DMP 82] von Koch, H. 7 von Neumann, J. 371 von Saarloos, W. [SK 87] Voss, R.F. [VC 78] [Vos [Vos 109 126 134 Wagon, S. [Wag 85] [KW Wall Street 126 Wallis, J.R. [MW 69] Wang, H. 326 Wang, N. [WCK 87] Wave diffraction 235 Weak nuclear interaction 106 Weather forecasting 167 Weber — Fechner law 70 Weber, E.H. 70 Weber, W. 70 124 Weber’s law 70 Weierstrass function 96 97 140 Weierstrass, K. 7 96 143 Weinberg, S. [BPS 87] Weiner, J. [Wei 90] Weitz, D.A. [WO 84] [SWGDRCL 232 Well-tempered instrument 101 Well-tempered scale 85 Wente, E.C 72 Wentzel — Kramers — Brillouin approximation 86 Werman, M. [WWM 87] West, J.E. [ASSW 66] [SASW Westervelt, R.M. [GW 87] [BW Weyl, H. [Wey 81] 17 40 White music 110 White noise 109 121 White, N.E. [HLSTLW 86] Whitehead, A.N. 301 Wiener process 140 Wiener, N. 140 145 Wiesenfeld, K. [BTW 87] [BTW 389 Wiesmann, H.J. [NPW 84] [NPW Wilson, K. 357 Wilson, R. 115 Wilson, T.A. [Wil 67] Wiltzius, P. [SMWC 84] Winding number 324 329 341 343 Wirtz, J. [AZL...89] Wisdom, J. [WPM 83] [Wis
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