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Kitchens B.P. — Symbolic dynamics: one-sided, two-sided and countable state markov shifts.
Kitchens B.P. — Symbolic dynamics: one-sided, two-sided and countable state markov shifts.

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Название: Symbolic dynamics: one-sided, two-sided and countable state markov shifts.

Автор: Kitchens B.P.

Аннотация:

This is a thorough introduction to the dynamics of one-sided and two-sided Markov shifts on a finite alphabet and to the basic properties of Markov shifts on a countable alphabet. These are the symbolic dynamical systems defined by a finite transition rule. The basic properties of these systems are established using elementary methods. The connections to other types of dynamical systems, cellular automata and information theory are illustrated with numerous examples. The book is written for graduate students and others who use symbolic dynamics as a tool to study more general systems.


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 252

Добавлена в каталог: 11.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\zeta$-block presentation      27
Adler, R.      1 4 5 6 7
Alphabet      21
Amalgamation      34 35
Amalgamation, column      73
Amalgamation, elementary      67
Amalgamation, row      73
Amalgamation, total      73
Amalgamation, total column      35
Amalgamation, total one-step amalgamation      67
Amalgamation, total row amalgamation      42
Artin, M.      1
Ashley, J.      2 3 4 5
Automorphism      63
Automorphism group      64
Away from zero, characteristic polynomial      25 108 109
Away from zero, core matrix      153
Away from zero, Jordan form      48 49 107 155
Baker, K.      2
Ballot Theorem      215 225 239
Berg, K.      1 5
Blanchard, P.      3
Block assignments      123 126 128
Block of symbols      21
Borel $\sigma$-algebra      159
Bowen — Franks groups      51 109
Bowen, R.      1 2 7
Boyle, M.      3 4 6
Cantor set      2 4
Capacity of a channel      30 189
Caratheodory extension theorem      161
Cellular automation      181
Cellular automation, reversible cellular automaton      182
Channel code      182
Characteristic polynomial away from zero      25 108 109
Coding, channel code      182
Coding, data string      184
Coding, decoder      187
Coding, encoder      183 187
Coding, encoder, coding theorem      189
Coding, rate      184
Compact-open topology      65
Compactification      229
Conjugacy, almost-topological      139 142
Conjugacy, self      66
Conjugacy, topological      33 54 232
Conjugacy, weak      110
Constrained string      184
Coppersmith, D.      6
Core Lattice Construction      153
Coven, E.      3 4 6
Cuntz, J.      2
Curtis, M.      1 3
Cylinder set      2 22
Decidable problem      44
Descending chain of subgroups      179
Devaney, R.      3
diamond      98 156
Dimension group      56 57 90 109
Direct limit      55
Direct sum      55
Distinguished coordinate      102
Edge coloring      105
Edge labelling      95
Eigenvector, approximate      184
Eigenvector, Perron      17 204
Embedding      95
Embedding, embedded subshift      120
Entropy of Markov measure      165
Entropy of partition      164
Entropy, absolute      30
Entropy, block      233
Entropy, capacity      189
Entropy, conditional      171
Entropy, Gurevich      232
Entropy, loop      232
Entropy, measure-theoretic      164
Entropy, Salama      233
Entropy, topological      23 98—99 120 140 142 151 165—166 174 182 228 230
Erdos, P.      7
Eventual image      48 53 182
Eventual kernel      48 53
Expected return time      198 205
Extension construction      116
Factor, of subshift of finite type      148
Factor, unequal entropy      126
Fatou's lemma      222 226
Fatou, P,      1
Feller, W.      7
Fibered product      138
Fiebig, D.      7
Fiebig,U.      7
Filler blocks      125 130
Finite approximation      221
Finite Approximation Theorem      199
Finite equivalence      139 140
Finite order      72 74 91
Finite state automaton      183 188
Finite subgroup      91
Finitely presented dynamical systems      188
First return map      70
Fischer cover      151 153 188
Fischer, R.      6
Follower set, of a symbol      34 105 178
Follower set, of a word      148
Forwardly expansive      182
Franaszek, P.      6
Franks, J.      2 3
Fried, D.      1 6
Friedman, J.      4
Full cover      149
Full shift      2 104
Full shift on countably many symbols      226
Furstenberg, H.      5
Generalized Perron — Frobenius Theorem      199
Generating functions      197
GL (n, Z)      58
Goodwyn, L.W.      4 5
Graph, automorphism      70 78
Graph, homomorphism      68
Graph, Shannon      188
Graph, strongly connected      3 16
Graph, transition      3
Group, center      87 91
Group, character      55
Group, combinatorial group theory      75
Group, composition factors      80 81
Group, composition series      80
Group, coset      178
Group, cyclic      76 91
Group, divisible      74
Group, duality      55 111
Group, extension      79
Group, factor groups      80
Group, finite      64 84
Group, finitely presented group      75
Group, free      75 91
Group, free product      91
Group, inverse limit      90
Group, Jordan — Holder Theorem      80
Group, normal series      79
Group, normal subgroup      178
Group, residually finite      65 91
Group, semi-direct product      80
Group, simple      74
Group, wreath product      80
Gurevich, B.M.      7
Gyration number      89
Hadamard, J.      1
Halmos, P.      6
Hassner, M.      6
Hedlund, G. A.      1 3 4
Higher block presentations      27
Hofbauer, F.      7
Horseshoe map      9
Information theory      165
Intrinsically ergodic      190
Inverse limit      53 109
Jordan form away from zero      48 49 107 155
Julia set      29
Julia, G.      1
Keen, L.      3
Kim, K.H.      2 3
Kitchens, B.      2 3 4 6
Koellmer      2
Kolmogorov, A.      1 5 6 7
Konheim, A.      1 7
Krieger cover      158
Krieger, W.      2 3 4 6
Landford, O.      1
Lattice Construction      106 156
Limit set      135
Lind, D.      1 3
Locally compact      227
Locally finite      227
Lyndon, R.      1 3
Machines      182
Magic symbol      113
Magic word      102
Magnetic disks and tape      182
Manning, A.      6
Mapping, block      25 26 232
Mapping, closing      114 120
Mapping, coding      182
Mapping, compatible      69
Mapping, constant-to-one      115
Mapping, degree      151
Mapping, exactly d-to-one      115
Mapping, factor      95 232
Mapping, finite-to-one      99 101
Mapping, indecomposable      118 120
Mapping, induced      113
Mapping, infinite-to-one      99 126
Mapping, one-to-one almost everywhere      103
Mapping, open      120
Mapping, permutive      64
Mapping, resolving      97 114 131 137 141 150 183
Mapping, unifiler      131
Mapping, word problem      75 91
Marcus, B.      4 5 6
markers      65 85 234 120 126
Marking a point      122 128
Markov approximation      164 234
Markov condition      5 6 7 12
Markov magic word      150
Markov partition      5 7 29
Markov property      8
Markov shift, countable state      226
Markov shift, cyclic subsets      223
Markov shift, cyclic subsets of indices      18
Markov shift, irreducible      22 227
Markov shift, mixing      182
Markov shift, nonwandering      22 137
Markov shift, period      100 142—143
Markov shift, reducible      136
Markov shift, topologically mixing      226
Markov shift, topologically transitive      226
Markov shift, transitive      22
Markov subgroup      177
Markov subgroup, classification      178
Markov subgroup, conjugacy      178
Markov subgroup, isomorphism      178
Markov subgroup, one-step      180
Markov weight set      168
Matrix, aperiodic      17 196
Matrix, compatible      162
Matrix, core matrix      154 189
Matrix, countable      195
Matrix, elementary divisors      52
Matrix, irreducible      3 16 196
Matrix, irreducible components      20 136
Matrix, maximal irreducible component      20 136
Matrix, null recurrent      197
Matrix, period      16 196 22
Matrix, positive recurrent      197
Matrix, principal submatrix      107
Matrix, probabilisticly transitive      198
Matrix, recurrent      197
Matrix, spectral radius      20
Matrix, stochastic      159 198
Matrix, subdivision      67
Matrix, transient      197
Matrix, transient state      20
Matrix, transition      4 36
Mazur, B.      1
McAndrew, M.      1 7
McMillan, B.      4
Mean recurrence measure      205
Mean recurrence weight      205
Measure, Borel probability      159
Measure, ergodic      162
Measure, Markov      161 234
Measure, maximal      166 174 188 234
Measure, mixing      162
Measure, n-step Markov      163 173
Measure, one-step Markov measure      161
Measure, support      161 234 237
Metric      2
Metric, compatible      228
Metric, complete      233
Metric, totally bounded      230
Metric, uniformly equivalent      229
Mixing      182
Morse, M.      1
Name of point      5
Nasu, M.      4 6
Natural extension      53
Noiseless coding theorem      189
Nonwandering set      29
O'Brien, G.L.      4
One-sided, automorphism group      91
One-sided, one-sided embedding      126
One-sided, one-sided full shift      2
One-sided, one-sided subshift of finite type      3
One-sided, one-sided topological Markov shift      3
Optical data storage disk      182
Ornstein, D.      5
P-name      5
Parry, W.      1 2 5 6
Paul, M.      4 6
Perron eigenvalue      17 19 140 223 230
Perron — Frobenius theorem      17 18
Petersen, K.      7
Points, asymptotic      114 113
Points, doubly transitive      3 22 101
Points, eventually periodic      2
Points, mutually separated      11 115
Points, nonwandering      22 135 182
Points, periodic      2 120 182
Points, preperiodic      2
Points, totally separated      115
Points, transitive      3 22 135
Points, wandering      135
Pollard, H.      7
Predecessor set of a symbol      33 178
Predecessor set of a word      148
Probabilistic walk      198
Random walk      215 216
Recoding      113
Recoding Construction      113
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