Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Gumowski I., Mira Ch. — Recurrences and Discrete Dynamic Systems
Gumowski I., Mira Ch. — Recurrences and Discrete Dynamic Systems

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Recurrences and Discrete Dynamic Systems

Авторы: Gumowski I., Mira Ch.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1980

Количество страниц: 272

Добавлена в каталог: 15.08.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
Abel, functional equation of      4 97
Accumulation of bifurcations      86
Admissible perturbations      18
Almost identity transformation      92 95 98 124
Analytical invariant curve (in the sense of Poincare)      67 70
Antecedent      12 29
Antecedent, half-trajectory      12
Antecedent, sequence      6
Asymptotic properties of cycles      112 113
Attractor, composite      216—219 223 233
Attractor, preferential (priviledged)      196 198 200—202 215
Attractor, strange      10 216 229 249
Automorphic function      4 46 67 210 245 246
Autonomous differential equation      17 18 101 102 104
Autonomous recurrence      2 10 11 15
Baker transformation      26
Bifurcation      6 21 36 33 40 94 115 129 136 146 187 196
Bifurcation, chain      37 40 178 208 216 224
Bifurcation, function      129
Bifurcation, leading to a regular closed invariant curve      26 91 95 216 225—
Bifurcation, leading to an invariant segment      38 43
Bifurcation, leading to the disappearance of a closed invariant curve      219 220
Bifurcation, scheme      36 37 115 119 130 133 144 168 177—179 213—216
Bifurcation, structure      41—43
Bifurcation, value      39 40 129 147 177 191 193 199
Biological model in the form of a recurrence      23 223
Birkhoff's, classes of functions      10
Birkhoff's, instability rings      17 105 110 111 115
Boettcher, functional equation of      4
Boundary, of a no-escape region      33 185 226
Boundary, of an influence domain      32—34 83 91 92 185
Box-within-a-box structure, in parameter space      41
Box-within-a-box structure, in phase space      177—179 196 201
Branching process      6
Canonical form      71—74 78 92 98 102 122 126 128 133 140 148 149 181
Centre      17 72—74
Centre, unstable      167 169
Chain of cycles      41
Chaos, generated by a first order recurrence      44
Chaos, generated by a second order recurrence      122 136 137 148 159 169 173 185 222—233 249
Chaos, in biology      23 223
Chaos, in economics      25
Chaos, in the sense of Poincare      19
Characteristic, equation      63 66
Characteristic, number (in the sense of Liapunov)      94
Characteristic, qualifiers      21 149
Characterization of a function by means of singularities      6
Cigala constants      92
Closed phase plane trajectory      3 91—94 177 216—221 225
Collective variables      12 20 104
Combinatorial explosion      29
Complex (or chaotic) dynamics      12 51 52 185
Composite, fixed point or cycle      47 50 149
Composite, stability region      34 36
Conjugate transformation      13 55 241
Consequent      8 29
Consequent, sequence      6
Conservation of symmetry      55
Continuous, dependence on data      19
Continuous, dynamic system      5 17 30 179
Control problem with hysterisis      63
Correctly set problem      19
Critical, critical case (in the sense of Liapunov stability)      17 30 36 47 122 132
Critical, curve      83 88 89 185 203 204 207 217 226 227
Critical, effective order      119 121
Critical, point (in the sense of Julia — Fatou)      12 32
Cusp      133 148 178 197
CYCLE      9 15 29
Cycle with unequal number of antecedents      204 205
Cycle, external      150—152 160—164 207
Cycle, internal      149—152 160—164
Cycle, mixed      154—159 164—169 173 197 198
Cycle, secondary      161
Cyclic curve segments      220
Damping threshold      215
Deterministic parity violation      54—57
Difference equation      4 65 66 69
Differentiation operator, non-integer      99
Diffusion region      122 152
Disappearance of homoclinic points      213
Discontinuity of antecedent invariant curves      204 207—210
Discrete (half-) trajectory      6
Discrete (half-) trajectory, located on an invariant curve      70 216 232
Discreteness of measurements      5
Disintegration of an island structure      117—119 143—146
Disorderiliness      14
Display of discrete trajectories      6 156 157 186 222 226
Dominant (or dominating) terms      76 123 124 126—129 181 191 194 203
Dynamic system, continuous      5
Dynamic system, discrete      5
Dynamics, complex or chaotic      20 122 136 152 153
Dynamics, orderly      41 51 52 58 81 212 216 249
Economic model      23—25 62
Effective order (or k/r ratio)      116 187 197 199 201 212
Eigendirections      71 77
Eigenvalue      30 66 94
Eigenvalue, problem for a functional equation      98 238—240
Eigenvalue, relation to stability      67 72
Equivalence, between recurrences and difference equations      4
Equivalence, between recurrences and differential equations      3 101—103
Ergodic theory      12 51 104
Exceptional case (in the sense of Cigala)      72 122 124 125 127 133—135 138 143 181 187 193 201
Excess, antecedent      46 81 203
Excess, antecedent curve      83
Excess, cycle      136
Feedback system (non linear)      26
Fixed point      8 15 29
Focus      17 73 74
Fractional iterate      17 70 71 96 100 101
Functional equation of automorphic functions      4 16 46 245
Functional equation of invariant curves      16 67—69 77
Functional equation of iterative square roots      255
Functional equation of translation      74 94
Functional equation, Abel      4 97
Functional equation, Boettcher      4
Functional equation, dependence on an arbitrary function      68 242
Functional equation, dynamically relevant      4 52
Functional equation, involving involutions      252—254
Functional equation, Perron — Frobenius      4 12 51 228 238 249 254
Functional equation, Picard      53 238
Functional equation, Schroeder      4 46 49 79 80 83 97 98 210
Functional equation, Schroeder, for an invariant segment      238
Functional iterate      4 9 13 97
General solution of a recurrence      52 238—239
Generating bifurcation      40 91 95 233
Germ of an invariant curve      76 77 229 232
Grossier (system or equation)      75 76
Hadamard, correctly set problem      19
Hat function      26 53 56
Heteroclinic point, accumulation point of cycles      115
Heteroclinic point, conservative      116 121 159
Heteroclinic point, N-type      195 196 199 201
Heteroclinic point, non conservative      194 197 218
Homoclinic point      110 112 113 116 133 144 155 159 193 232
Homoclinic point, accumulation point of cycles      113 115 152 177 197 199 200
Image cycle      169
Implicit function theorem      181
Inert (system or equation)      75 76
Influence domain      30 56 81—91 193
Influence domain, analytical      83—85 87
Influence domain, composite      34 40 50 90 184 185 227
Influence domain, immediate      13 31 47 49 87 98
Influence domain, multiply connected (or disjoined)      30—31 49 87—89
Influence domain, singly connected      30
Influence domain, total      31 33 81 87 93
Instability ring (of Birkhoff)      17 105 110 111 115
Invariant angle (or direction)      125—128 140 201
Invariant curve      16 67 70
Invariant curve, analytical (in the sense of Poincare)      67 70
Invariant curve, antecedent branch      83
Invariant curve, closed      91 94 177 216—221 225
Invariant curve, consequent branch      83
Invariant curve, coordinate dependence      68
Invariant curve, dependence (apparent) on an arbitrary function      70
Invariant curve, excess antecedent branch      203 207—210
Invariant curve, explicitly known      101 252—256
Invariant curve, functional equation of      16 67—69 77
Invariant curve, main      112 122 137 148 174 203
Invariant curve, parametric description      70
Invariant curve, regular      79 81 135 177
Invariant curve, relation to the Schroeder equation      79
Invariant curve, S-loops of      192—194 198 216
Invariant curve, self-intersecting      203 208—210 217 218 222
Invariant curve, separation into branches      69
Invariant curve, singular      67 79 82 131 177
Invariant curve, stability of      94
Invariant density      12 14 50 56 227 228
Invariant manifold      7
Invariant segment      9—11 17 32 34 38 40 238
Invariant segment, cyclic      33 43—46 56 57 240 241
Inverse recurrence      11
Involution      239 251—255
Island structure      110 115 136 137 144 153
Iterate, continuous      17 70 71 96—98 100 101
Iterate, fractional      17 70—7 1 96—98 100 101
Iterated recurrence      8 15 17 29
Iteration of quadratic polynomials      23 96
Iterative square root      96 97 255—257
Jacobian determinant, equal to unity      61 102 104 182 252
Jacobian determinant, non vanishing, not implying unique antecedents      181 182
Jacobian determinant, vanishing      12
Julia — Fatou theorem (on critical points)      32 40
Koenigs — Lemeray staircase construction      30
Liapunov V-function      81 196
Limit cycle      3 26 64
Linear differential equation with periodic coefficients      63 65
Linear recurrence      2 17 30 47 65—75 100
Liouville's theorem (area conservation)      104 184 254
Logarithmic convexity      99
Longitudinal motion of a particle      61
Lorenz problem (meteorology)      25
m-th order form      123 152
Macroscopic variables      12
Main fixed point      112 122 137 148 174 187 191 194 195 197 198 201 216
Main invariant curve      112 140 159 160 169 174 187 189 190
Mean mass density      50 56 227 228
Mean mass density, equation of      54 228
Microtron      61 174
Myrberg recurrence      38 96 237 240 257
No-escape region      33 36 50 156 157 184 223 226 228—233
No-escape segment      12 36
Node, (simple)      17 71 73 77
Node, critical      75 77 80
Node, di-critical (or star-node)      74 75 80
Non homogeneous linear functional equation      78 79
Non linear feedback system      26
Open optical resonators      61
Orderly dynamics (or motion)      41 51 52 58 81 212 216 249
Perron — Frobenius functional equation      4 12 51 211 228 238 249 254
Perturbation, admissible      18 21
Perturbation, non linear      17 76 79 102
Perturbation, structural      20
Phase (space) cell      14 79 109 123 159
Phase advance (or rotation angle)      67
Piecewise linear recurrence      25 52
Poincare's surface of section      2 64 179
Point of alternance      83 85 88 207—210 217
Point singularity      7 15 16
Point singularity, stochastic      250 251
Point singularity, types of      17
Points of a stability boundary      31 83
Polynomials of Myrberg      38
Population dynamics      23 62 223
Preferential attractor      196 198 200—202
Pseudo-eigenvalue      59
Quadratic polynomials, iteration of      23
Quadratic recurrence, first order      38 96 237 240 257
Quadratic recurrence, second order      106—137 187—201 216—223 229—233
random number generation      10 15 27
Randomness, relation to Birkhoff's function classes      14
Randomness, relation to topological entropy      14 59 60
Randomness, tests      14 59 60
Recurrence      2 15
Recurrence, biological model      23 62 223
Recurrence, bounded quadratic      106 148—159 197—201 212
Recurrence, cubic      106 137—148 201
Recurrence, cycle of      9 29
Recurrence, economic model      23—25
Recurrence, explicitly known invariant curves of      101 252—256
Recurrence, explicitly known solutions      44 237—239 242 243
Recurrence, exponential      106 159—169
Recurrence, fixed point of      8 29
Recurrence, general solution      3 15
Recurrence, generic examples      5
Recurrence, inverse      11
Recurrence, iterated      8 15
Recurrence, linear      2 65—75
Recurrence, piecewise linear      25
Recurrence, quadratic      38 96 106—137 187—201 216—223 229—233 237 240 257
Recurrence, sinusoidal      106 169—173
Recurrence, sinusoidal unsymmetric      106 173—176
Recurrence, solution of      3
Recurrence, solution of, analytic definition      5
Recurrence, solution of, Cauchy problem      4 6
Recurrence, solution of, explicit known      44 66 237—239 242 243
Recurrence, solution of, indirect definition      6
Recurrence, solution of, operational definition      6
Recurrence, solution of, relation to fractional and continuous iterates      244 256 257
Recurrence, solution of, relation to solutions of some functional equations      52 97 238 239
Recursive system of equations      50 54 77 80 100 149
Redundancy tests      82 105
Regularization of an incorrectly set problem      20
Resonance, harmonic      9 63
Resonance, main      9 72
Resonance, subharmonic      9 29 63
Resonance, weak      74 187
Rotation angle (or phase advance)      67 72 146 169
Rotation number      108 109 112 159 187 196 199 229
Rotation sequence      45 229
Saddle (simple)      17 72 73
Saddle (simple), multibranch      127 128 136 181 201
Schwarzian derivative      33
Secular terms in functional equations      55
Segment without contact      28
Sensitivity analysis      20
Sensitivity coefficients      20 45 59 220 237 247 248
Separatrix      79 105
Sequence of antecedents and consequents      6
Servo with feedback      23
Singularity of a recurrence      6 7 69 71 97
Singularity structure      6 14 18 20 36 38 44 45 200 220
Singularity structure, composite      7 219 221
Singularity structure, elementary      7
Singularity structure, generic      21
Small parameter expansion      49 54 55 73 92—94 191 193 199
Solution of a recurrence      see "Recurrence solution
Stability (in the sense of Liapunov)      29 94
Stability domain      see "Influence domain"
Stagnation of discrete trajectories      216
Star-node      27 28 74 75 80 83 84
Stationary state      7—10 234
Stationary state, Birkhoff's classification      10
Stationary state, orderly      see "Orderly dynamics"
Stationary state, qualitative change      26 27
Stationary state, stability of      8 9
Stationary state, stochastic (or chaotic)      12—14 17 27 28 see
Statistical physics      12 14 104
Statistical tests      see "Randomness tests"
Stochastic instability (and region of)      122 136 152 153
Stochastic point singularity      250 251
1 2
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2017
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте