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