Denker M., Grillenberger Ch., Sigmund K. — Ergodic Theory on Compact Spaces :: Электронная библиотека попечительского совета мехмата МГУ

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Denker M., Grillenberger Ch., Sigmund K. — Ergodic Theory on Compact Spaces

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Название: Ergodic Theory on Compact Spaces

Авторы: Denker M., Grillenberger Ch., Sigmund K.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1976

Количество страниц: 360

Добавлена в каталог: 13.08.2008

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Предметный указатель

$(F,\Psi)$ -tower      254
$(m,\sigma)$ -spanning      84
$(n,\varepsilon)$ -separated      83
$(\alpha,\Psi)$ -name      51
$(\alpha,\Psi,n)$ -name of a point      51
-topology      225ff.
-topology, structurally stable      226
$G_\delta$ -set      12
$\epsilon$ -capacity      83
$\Psi$ -invariant      23
$\sigma$ -algebra      3
Abramov, theorem of      265
Absolutely continuous      24
Affinity of entropy      61
Almost periodic point      261
Alphabet      37
Anosov diffeomorphism      228
Aperiodic      7
Aperiodic matrix      47
Aperiodic state      47
Asymptotically h-expansive      162
atom      5
Atom of a partition      49
Automorphism of the torus      234
Automorphism of the torus, hyperbolic      239
Axiom A diffeomorphism      229
Baire’s theorem      12
Basic part      126
Basic part, set      124 230
Bernoulli measure      42
Bernoulli measure, shift      42
Birkhoff      20
BLOCKS      37 258ff.
Blocks, centred      37
Blocks, juxtaposition of      258
Blocks, M-transition      267
Blocks, number of      259
Blocks, occurrence of      37
Blocks, relative frequency of      258
Blocks, set of blocks = B1      258
Bogoliubov      18
Borel- $\sigma$ -algebra      8
Borel- $\sigma$ -algebra, set      8
Bowen      230
Bowen, measure      210
Breiman      79
Canonical coordinates      241
Canonical coordinates, hyperbolic      241
Choquet      78
CO-measure      195
Complete measure space      3
Completion of a $\sigma$ -algebra      4
Conditional entropy      62
Conditional top. entropy      160ff.
Conjugate, m.th.      5
Conjugate, top.      19
Conjugate, weakly m.t.      71
Continuity set      93
Continuity set, partition      93
Contraction      86
Covering dimension      134
Cylinder, centred      37
Decomposition, ergodic      230
Defining system of blocks      120
Differentiable map      224ff.
Dimension, covering      134
Dinaburg      134
Dynamical system ,top.      18
Dynamical system, m.t.      5
Elementary part      230
Embedding, pointwise strictly ergodic, minimal      316
Embedding, strictly ergodic      300
Entropy of $\Psi$       60
Entropy of a partition      56
Entropy of a partition w. resp. to $\Psi (h(\alpha,\Psi))$       59
Entropy of an ergodic decomposition      77
Entropy of Bernoulli shifts      69
Entropy of Markov measures      69
Entropy, $\epsilon$ -entropy      83
Entropy, absolute      82
Entropy, conditional      62
Entropy, conditional top.      160ff.
Entropy, expansive      162
Entropy, expansive, asymptotical      162
Entropy, expansive, locally      173
Entropy, maximal      147
Entropy, metric      63
Entropy, topological      83ff.
Equilibrium state      147
Equivalence of states      123
Ergodic      23
Ergodic decomposition      73ff.
Ergodic decomposition of entropy      77ff.
Ergodic fibre      73
Ergodic, intrinsically      156
Ergodic, strictly      34 261
Ergodic, totally      23
Ergodic, uniquely      27 261
Excluded block system      118
Expansive constant      104
Expansive constant homeomorphism      103
Extended transformation      17
Extremal      24
Factor, m.t.      6
Factor, top.      19
Finer, cover      82
Finer, cover, mod 0      50
Finer, cover, partition      49
Finer, cover, partition finer than a cover      106
Finitary (P-, F-)      252
Finite type      118
First category      12
Frobenius      42
Function, invariant      23
G-admissible subshift      252
Generating sequence      51
Generating sequence under $\Psi$       51
Generator      52
Generator for T      103
Generator, M-      261
Generator, natural      107
Generator, power of a      103
Generator, strong      52
Generator, topological      92
Generic point      20
Goodman      138
Goodwyn      134
Group automorphisms      150
Group automorphisms translations      28
H-expansive      162
Haar measure      29 150 234
Hansel      322
Hausdorff metric      111
Hedlund      38
Homeomorphism, contracting      86
Homeomorphism, isometric      86
Homeomorphism, Lipschitz      87
Homogeneous      149
Homomorphism, m.t.      6
Homomorphism, top.      19
Hyperbolic automorphism      239
Hyperbolic automorphism, fixed points of a      226
Hyperbolic automorphism, matrix of a      239
Hyperbolic automorphism, with canonical coordinates      241
In-set $(\delta-)$       226(241)
Individual ergodic theorem      20
Induced m.t. system      6
Induced m.t. system transformation      6
information      56
Intrinsically ergodic      156

Irreducible matrix      42
Isomorphic      4 5
Isomorphism, m.t.      3 4
Isomorphism, m.t., top.      19
Jewett      301
Kac      264
Katznelson      238
Kolmogorov      41 65 67
Krein      25
Krengel      52 263
Krieger      282 301
KRYLOV      18
Kushnirenko      225
Lebesgue space      4
Lebesgue — Stieltjes measure      4
letter      37
Lipschitz condition      87
Local product structure      246
Locally entropy, expansive      173
M-generator      261
M-partition      261
M.th. conjugate      5
M.th. conjugate, conjugate, weakly      71
M.th. conjugate, dyn. system      5
M.th. conjugate, isomorphism      4
Map, measurable      3
Map, measure preserving      3
Markov measure      43
Markov measure partition      246
Markov measure shift      43
Matrices, aperiodic      47
Matrices, irreducible      42
Matrices, period of      47
Matrices, positive      42
Matrices, related      250
Matrices, stochastic      43
Matrices, strongly shift equivalent      250
Matrices, transition-      121
Maximal entropy      147
Maximal entropy oscillation      207
McMillan      79
Measurable map      3
Measurable map set      3
Measurable map space      3
Measure      3
Measure of maximal entropy      147
Measure preserving map      3
Measure space      3
Measure theoretical dyn. system      5
Measure, Bernoulli      42
Measure, Bowen      210
Measure, CO-      195
Measure, complete      3
Measure, conditional      3
Measure, conjugate      5
Measure, ergodic      23
Measure, Haar      29 150 234
Measure, homogenous      149
Measure, isomorphic      5
Measure, Markov      43
Measure, Parry      130
Measure, point-      11
Measure, regular      8
Measure, T-homogenous      149
Measure, transported      5
Meshalkin      71
Metric of partitions      63
Metric, Hausdorff      111
Metric, Prohorov      11
Milman      25
Minimal      34 261
Minimal set      34
Minimal top.dyn.system      34
Mixing top. (strongly, weakly)      31
Mixing, mt. (strongly, weakly)      30
Morse — Smale — diffeomorphism      227
Nikodym      24
Nonatomic      12
Nonwandering point      34
Nowhere dense      24
Occurrence      37
Occurrence, dense      260
Occurrence, regular      260 261
Orbit (closure)      259
Order of a subshift      118
Ornstein      71
Out-set ( $\delta$ -)      227 (241)
Parry measure      130
Partition      49
Partition, atoms of a      49
Partition, continuity-      93
Partition, M-      261
Partition, refinement of a      49 50
Partition, return time      264
Period of a state      42
Periodic matrix      95
Periodic matrix point      95
Perron — Frobenius      42
Poincare’s recurrence theorem      6
Point measure      11
Positive matrix      42
Power of a generator      103
Pressure function      141
Probability vector      42
Product m.t.system      6
Product transformation      6
Prohorov metric      11
Pseudo-metric for partitions      50
Pseudo-orbit      232
Quasi-generic      20
Quasiregular point      21
Radon      24
Rationally dependent      239
Recurrence theorem      6
Refinement mod 0      50
Refinement of open covers      82
Refinement of partitions      49 50 106
Regularity property      8
Related matrices      250
Residual      12
Riemannian structure      224
Riesz representation theorem      9
Robbin      229
Rohlin set      7 254
Rohlin, lemma of      7 255
Rotation, irrational      29
Saddle      226
Scheller      262
Separating almost all points      51
Set, invariant      23
Set, measurable      3
Shannon — McMillan — Breiman      79
Shift      36
Shift, Bernoulli-      42
Shift, maps commuting with the      38
Shift, Markov-      43
Sinai      71
Sink      225
Smale      230
Sofic subshift      252
Source      226
Specification property      193
Spectral decomposition theorem      230
State space      36
Statistical ergodic theorem      20
Stochastic matrix      43
Strictly ergodic      34
Strictly ergodic embedding      300
Strictly transitive point      261
Strongly mixing, m.t.      30

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