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Baladi V. — Positive Transfer Operators And Decay Of Correlations
Baladi V. — Positive Transfer Operators And Decay Of Correlations



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Название: Positive Transfer Operators And Decay Of Correlations

Автор: 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.
This book, addressed to mathematicians and mathematical (or mathematically inclined) physicists, shows how the powerful technology of transfer operators, imported from statistical physics, has been used recently to construct relevant invariant measures, and to study the speed of decay of their correlation functions, for many chaotic systems. Links with dynamical zeta functions are explained.

The book is intended for graduate students or researchers entering the field, and the technical prerequisites have been kept to a minimum.


Язык: en

Рубрика: Физика/Нелинейная динамика, Хаос/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 314

Добавлена в каталог: 22.07.2005

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