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Baladi V. — Positive Transfer Operators And Decay Of Correlations
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Название: Positive Transfer Operators And Decay Of CorrelationsАвтор: Baladi V. Аннотация: Although individual orbits of chaotic dynamical systems are by definition unpredictable, the average behavior of typical trajectories can often be given a precise statistical description. Indeed, there often exist ergodic invariant measures with special additional features. For a given invariant measure, and a class of observables, the correlation functions tell whether (and how fast) the system "mixes", i.e. "forgets" its initial conditions.
Язык: Рубрика: Физика /Нелинейная динамика, Хаос /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2000Количество страниц: 314Добавлена в каталог: 22.07.2005Операции: Положить на полку |
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a.c.i.m. 73 75 123 148 197 Absolutely continuous 37 73 Absolutely continuous, measure 73 75 123 197 Absolutely continuous, stable foliation 236 Anosov diffeomorphism 228 Aperiodic matrix 3 Arzela — Ascoli theorem 38 153 Asymmetric norm 177 Atom (measure) 155 159 160 Attractor, hyperbolic 231 Axiom A 229 Basic set 231 Birkhoff, cone 68 75 141 212 219 223 242 288 Birkhoff, ergodic theorem 20 Birkhoff, inequality 76 Bound period 188 191 Bounded variation 149 Bowen, condition 60 Bowen, weight 61 Canonical product 230 Canonical system of conditional measures 234 Central limit theorem ix 168 Closing Lemma 229 Collet — Eckmann 184 Compact operator 31 Conditional expectation 160 Cone 4 (see also “Birkhoff cone”) Conformal measure 158 Convolution, random perturbation 169 Correlation, function 23 24 50 54 63 82 94 102 122 168 171 186 211 216 246 278 Correlation, function, Markov chain 122 Correlation, function, random skew product 138 Correlation, operational 278 Correlation, spectrum 57 139 168 245 246 Coupling 217 Critical point 145 Cylinder 11 Distortion 89 188 190 195 215 262 Dual (Banach space, linear operator) 32 Entrance time 143 Equicontinuous family 38 Equilibrium, measure 18 Equilibrium, state 18 86 137 158 Equilibrium, state, relativised variational principle 136 Ergodic basin 233 Escape, rate 109 142 Escape, time 193 Exact measure 21 186 204 216 Expanding map 71 Expansive homeomorphism 17 Feigenbaum conjecture 107 flows ix Fredholm, determinant, dynamical 31 101 105 113 Fredholm, determinant, Grothendieck 99 Fredholm, kernel 98 Fredholm, operator 67 Free energy 19 Fully cyclic 163 Gauss map 106 Generating partition 168 Gibbs 19 Gibbs, state 86 Gibbs, u-measure 239 Greatest common divisor of return times 204 215 258 Grothendieck — Fredholm operator 99 Half-inverse 272 Hausdorff dimension 109 142 Henon map 184 Hyperbolic, analytic map 271 Hyperbolic, attractor 244 Hyperbolic, diffeomorphism 228 Hyperbolic, measure 228 Hyperbolic, time 222 229 Hyperbolic, toral automorphism 225 Index (eigenvalue) 3 30 Intermittency 211 Invariant measure 13 Irreducible matrix 2 Iterated function system 140 Jacobian 73 111 160 Joint return 218 Julia set 110 Kneading operator 221 Large deviations 198 Lasota — Yorke bound 34 77 96 204 Lattice (integrally closed vector) 76 Lebesgue measure 72 Local product structure 230 Local stable leaf 288 Locally constant 16 Logistic family 185 Lyapunov exponent 88 93 185 228 Markov, chain 122 169 Markov, partition 100 114 239 243 Markov, partition, refinement 114 Markov, property 114 195 214 Markov, rectangle 243 Mixing 21 83 Mixing, topological 13 72 Multiplicity (eigenvalue), algebraic 3 30 Multiplicity (eigenvalue), geometric 3 30 Multiplier 110 Natural extension 53 Natural measure 73 232 291 Nonwandering set 229 Nuclear operator 99 Nuclear operator, order 98 Nuclear operator, trace 99 Nussbaum’s formula 32 Operator norm 30 Order (entire function) 99 Oseledec theorem 228 Parabolic point 223 Partial inverse 271 Partial order 75 Partial order, continuous 76 Partially hyperbolic 231 Partition function 19 Period (of a matrix) 3 Peripheral spectrum 163 Perron eigenvalue 3 Perron — Frobenius theorem, finite dimension 4 Perron — Frobenius theorem, infinite dimension 36 Pesin theory 233 Physical measure 73 232 291 Pinning coordinates 272 Positively expansive 17 60 Pressure 19 Proper set 243 Pseudo-orbit 230 Quadratic family 185 Quasi SRB measure 238 Quasicompact 31 34 84 88 155 Radon measure 26 Random skew product 135 Real analytic rectangle 282 rectangle see “Markov rectangle” Regular, discontinuity 151 Regular, set function or measure 14 Relative entropy 137 Relativised variational principle 137 Renormalisation 107 Repellor 108 142 Repellor, analytic 110 Repellor, hyperbolic 231 Resonances 57 246 Riesz representation theorem 33 Rohlin formula 160 Roundoff error 119 Ruelle — Perron — Frobenius transfer operator 29 s/u-subsets 249 Schwarz lemma 271 Schwarzian derivative 185 Semisimple 30 Sensitive dependence 119 Separation time 194 214 250 Shadowing lemma 230 Sharp, determinant 220 Sharp, trace 221 Skew product 136 Specification 60 Spectral, decomposition 114 230 235 Spectral, radius 30 Spectral, radius, essential 30 Spectral, radius, formula 14 31 Spectral, stability 124 126 171 178 Spectrum 30 Spectrum, essential 67 SRB measure 73 119 233 SRB measure, formal definition 234 Stable discs 248 Stable discs, formal definition, continuous family 248 Stationary probability vector 13 Stochastic matrix 13 Stochastic stability 119 124 171 Subshift of finite type 11 Superexponential decay of correlations 102 226 Support (of a measure) 15 Symbolic dynamics 72 86 100 243 Telescoping function 118 Topological pressure 18 19 47 159 Topologically, mixing 13 72 Topologically, transitive 12 Total variation 26 Total variation (of a measure) 149 Tower 195 214 249 Tower, extension 148 184 186 Transfer operator 25 29 221 Transfer operator, dual 73 Transfer operator, hyperbolic 275 Transfer operator, normalised 29 Turning point 145 Unimodal map 184 Unstable, discs 248 Unstable, discs, continuous family 248 Unstable, foliation 233 234 247 Unstable, manifold, global 233 Unstable, manifold, local 229 234 Upper bound on mixing 83 Variation, total (of a measure) 149 Variational Principle 17 20 Variational principle, relativised 136 Variational principle, weighted 18 Volume lemma 111 Wandering state 3 Weak-* topology 32 33 Zeta function 28 58 101 105 139 142 169 222 243 269
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