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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
Nonlinear dynamics 357 Nonlinear mechanics 172 Nonlinear oscillator 67 Nonlinear physics 338 Nonlinear problem 243 Nonlinear system 185 Nonlinearity 175 Nonnormal irrational number 241 Nonperiodic orbit 183 Nonstandard statistics 160 Nonzero Lebesgue measure 183 Normal law of probability 113 Normal mode 43 Normal number 241 Nuclear force 106 389 Nuclear fragmentation 356 NUMBER 161 Number of molecules 144 Number system 47 Number theory 100 Number-theoretic fluke 101 102 Numerical divergence 244 Numerical precision 244 Octave 97 99 101 122 Odd period length 285 Odd-parity cover 382 Odds 148 150 207 208 Oliveria, M. [WO 84] 232 One-hump (unimodal) map 285 One-to-one mapping 164 Onoda, G.Y. [OT 86] optical fiber 159 Orbit 40 166 240 269 Orbit interpolation 285 Orbital period 67 171 Order parameter 347 Ostrowsky, N. [SO 85] Ottino, J.M. [Ott 89] Outguessing machine 149 Page, W. [Pag 81] Pagels, R. 357 Painting turtle state 259 Paired comparison 76 Pais, A. [Pai 82] Pallas 171 Paper folding 45 Paradox 97 155 157 Paradoxical self-similar waveform 96 Paradoxical sound 95 Parallel mirror 82 Parallel processing 167 363 372 Paramagnetic 346 Parameter sensitivity 185 Parametric amplifier 171 Parenting of orbits 282 Pareto, V. [Par 1896] 34 Parity 279 376 Parker, R.L. [AZL...89] Parlitz, U. [LP 88] Partial differential equation 69 Particle velocity 372 Partition function 206 Pascal’s triangle 386 Passajo, D. [MPP 84] Passoja, D. 230 Pauli, W. 230 350 Pauling, L. [Pau 85] 302 Paullay, A. [MPP 84] 230 Peale, S. [WPM 83] Peano, G. 13 187 Peitgen, H.-O. [PR 84] [PPR [PR [PR [PS 244 299 363 Penrose tiling 265 313 Penrose, R. [Pen 74] Penzias, A. 115 Perceived weight 71 Perceptual paradox 95 Perceptual space 77 Percolating cluster 31 33 Percolation 30 39 345 355 Percolation threshold 30 345 Perera, A.G.U. [CMP 87] Perfect fifth 99 Perfect set 162 Perimeter 41 354 Period doubling 208 271 273 275 Period-3 279 291 Period-doubling bifurcation 279 Period-tripling operator 284 Periodic binary number 240 Periodic crystal 302 Periodic point 24 257 Periodic window 279 281 291 periodicity 98 319 Perrin, J.B. 8 140 144 Pfeifer, P. [PA 83] 236 Phase locking 171 Phase space 253 267 320 Phase space trajectory 324 Phase transition 353 357 Phonon 43 Photon 43 106 189 Photon statistics 334 Phylogenetic tree 87 Physically realizable inverse 77 Pi value 257 Pi-meson 106 Picture recognition 57 Piecewise linear function 249 Pierce, J.R. [ZLP 76] [Pie [MPRR 101 102 114 Pietronero, L. [NPW 84] [NPW [PS Pimm, S.L. [RP 88] Pink music 110 Pink noise 34 109 111 122 125 Pinkham, R.S. [Pin 62] Pion 106 Pipe model 117 Piran, T. [BPS 87] Pitch 95 122 Planck length 33 107 Planck’s constant 112 Planck’s law 189 Planetary system 27 Plath, P.J. [DGJPS 85] Pluto 25 Poincare mapping 243 Poincare section 324 Poincare, H. 25 187 Point process 152 Point set 39 Poisson distribution 190 Poisson process 71 Pomeau, Y. [DGP 78] Population dynamics 167 Population variation 131 potential energy 66 67 Potential theory 198 Power law 31 33 103 184 227 350 356 389 Power spectrum 121 122 123 144 Power-law distribution 103 Power-law noise 126 Power-law relation 71 Power-law scaling 390 Practical fractal 211 Prediction residuals 127 Preference space 75 Preimage 39 244 Preperiodic binary fractions 240 Prime factor 363 Prime number 101 Prime-number decomposition 164 Primitive polynomial 79 236 Primitive root 236 Primitive scaling factor 93 Probability amplitude 151 probability distribution 188 203 Probability theory 157 171 Procaccia, I. [GP 83] [HP [HP [HP [JKLPS [HJKPS [PTT 232 334 342 Projection 181 183 Projection method 312 Proof by self-similarity 93 94 Proper fraction 48 Pruefer, M. [PPR 85] Prusinkiewicz, P. [Pru 87] 261 pseudorandom number 258 psychoacoustics 71 123 Psychological scaling 70 74 Psychophysics 71 Psychovisual mode-locking 34 Purcell, E.M. [Pur 77] 70 Purkert, W. [PI 87] Pyenson, L. [Pye 85] Pythagoras’s theorem 3 Pythagorean comma 101 Quadratic irrational number 319 Quadratic map 207 268 291 Quadratic potential 66 Quadratic residue 79 236 Quantum gravity 106 Quantum mechanical vacuum 114 quantum mechanics 122 133 Quasar 155 Quasi-stellar object 155 Quasicrystal 57 302 304 310 312 315 319 325 Quasiperiodic lattice 57 310 312 Quasiperiodic spin 329 Quasiperiodicity 319 Quintic algorithm 258 Rabbit constant 55 Rabbit lattice 311 Rabbit mapping 56 Rabbit sequence 55 306 308 309 311 315 329 Rabi, I. 106 Radar clutter 44 Radar intensity 33 Radiation density 115 Radioactive decay 389 Radon transform 135 Radons, G. [GZR 87] Raimi, R.A. [Rai 76] Ramanujan, S. [Ram 14] 239 257 Rammal, R. [RTV 86] Random fractal 30 196 Random interference 73 Random noise 320 Random number 125 Random resistor network 367 Random sequence 150 359 Random walk 145 146 350 Rank-ordering 147 Ratio scale 71 Rational approximation 100 Rational frequency ratio 172 324 Rational function 40 244 Rational function of frequency 226 Rational numbers 163 Rayleigh — Benard experiment 277 Reaction rate 387 Real number 163 Real-time computation 150 Reality of atoms 144 Reciprocal scaling 113 Reciprocity failure 65 Recursive computation 99 Redfearn, A. [RP 88] Redundancy 35 127 Reeves, A. [MPRR 88] Reflection phase grating 79 236 Relativity 113 Relaxation process 123 Remodeling 69 renaming 265 Renormalization 357 367 Renormalization theory 265 306 342 361 Renormalized lattice 368 Renyi, A. [Ren 55] 203 Repellor 40 244 271 Rescaled range 129 Rescaling 33 Resonance 40 Resonant mode 69 Response fluctuation 73 Response maximum 73 Rest mass 106 Reverberation time 73 74 125 Reverse bifurcation 279 281 Reynolds number 70 277 Richter, P.H. [PR 84] [PPR [PR [PR [RS 299 363 Riemann, B. 336 Risset, J.-C. [Ris 71] [Ris Robbins, M.O. [SWGDRCL 86] Roberts, L. [MPRR 88] Roeschke, J. [Roes 86] Romaides, A.J. [JER 90] Room resonance 73 Rosenfeld, A. [RK 82] 57 Rotating cylinder lens 134 Rotational symmetry 302 Rough surface 227 Roulette 128 150 Rouse, H. [RI 57] Ruin 152 Ruin-free time zones 153 Run length 57 Russell, B. 301 Russian dolls 81 383 Saddle point 256 Safe square 54 Sagher, Y. [Sag 89] Salem, J. [SW 86] Sander, L.M. [WS 83] 198 Sanz, J.L.C. [SHJ 88] Sasagawa, G. [AZL...89] Satanic staircase 174 Saturn 316 338 Saupe, D. [PS 88] 134 244 Sawtooth map 249 Scale factor 122 Scale model 69 Scale-invariant 390 Scaling 356 360 Scaling difficulty 69 Scaling exponent 184 201 347 Scaling factor 93 153 Scaling failure 65 Scaling invariance 122 304 330 Scaling law 63 216 329 330 347 Scaling test 71 Scattering angle 235 Scattering fractal 44 Scattering surface 79 Schaefer, D.W. [SMWC 84] 232 Schellnhuber, H.J. [NS 89] 245 Schmidt, P.W. 236 Schmitt, F.O. 38 Scholz, H.-J. [RS 87] Schroeder, M. [Schr 54] Schroeder, M.R. [Schr 64] [ASSW [SASW [Schr [Schr [Schr [Schr [SGS [SA [Schr [Schr [Schr Schuster, H. [DGJPS 85] Schuster, H.G. [Schu 84] Schwartzian derivative 286
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