Bogaevski V.T., Povzner A. — Algebraic Methods In Nonlinear Perturbation Theory :: Электронная библиотека попечительского совета мехмата МГУ

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Bogaevski V.T., Povzner A. — Algebraic Methods In Nonlinear Perturbation Theory

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Название: Algebraic Methods In Nonlinear Perturbation Theory

Авторы: Bogaevski V.T., Povzner A.

Аннотация:

This book will be of interest for everybody working on perturbation theory in differential equations. The book requires only a standard mathematical background for engineers and does not require reference to the special literature. Topics which are covered include: matrix perturbation theory; systems of ordinary differential equations with small parameter; reconstruction and equations in partial derivatives. Boundary problems are not discussed in this volume. The reader will find many examples throughout the book.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 265

Добавлена в каталог: 17.12.2009

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Предметный указатель

Accuracy of a system      78—79 81 110
Adiabatic invariant      50 122
Adiabatic invariant,transverse      65
Airy equation      151 177 182 243
Airy function      151 182 234 243
Asymptotic series      146—148
Basic function      22 24 28
Basic system of functions      21—24 28 33 36 43 48 52 55 58 59 64 66 79 120 142 143 200
Bifurcation      98
Bogolyubov — Krylov averaging method      51 54 61
Bogolyubov’s formulation/scheme/method      36 40 202 210
Bounded in height      7 8 24 34 132 165
Braginski corrections      64
Branching equation      96 100—102 104
Burger’s Equation      247 254
Canonical form (of an operator)      21—23 33—35 48 56 83 91 105 111 128 138 173 176 179 200
Center manifold theorem      83
Centrifugal drift      65
Change of variables operator      19 62 91
Chapman — Enskog method      40
Clebsch — Gordan formulas      32
Commutation relation      5 7 28 50 62 63 121
Commutator (of two operators)      3 18 43
Continuous system      78—79 82
Cyclotron frequency      61
Cyclotron frequency,local      61
Density of an operator      196 197
Derivative (of operator wrt an operator)      3 24 29 131
Diagonal operator/diagonal form of an operator      1 4 5 9 21 22 28 30 32 35 67 116 119 120 127—130 134 141
Differentiation of the commutator      3
Dirac theorem      44—45
Drift equations      61 64
Drift equations,system of      62
Drift trajectories      62 64
Eigenfunction (of an operator)      20 22 25 27 36 40 43 45 48 50 52 54 58 60 64 66 68 69 71 73 77 83 90 97 101—104 119 121 135 140 160 168—170 172 176 179 181 184 200 208 210 222
Eigenoperator      60 63
Eikonal equation      74 206—210 213 226 240
Electric drift      65
Euler motion (by inertia)      118 120—122
Euler — Poisson equations      116
Extended basic system of functions      22 28 129
Extended basis      24 26 27
Extended Jordon basis      23 24
Extended operator      22 65—67 125 163 167
Extended system      29 67 123 125
Fredholm alternative      99
Functional derivative      195
Gradient drift      65
Grassmann algebra      220
Hamiltonian operator      42 43 89 91—93
Hamiltonian system      89 214 228
Hausdorff formula      3 18 141
Height (of an operator)      4 5 9—11 32 35 132 135 172 176
Hilbert method      40
Hopf — Cole solution      254
Hopf's solutions      95
Hopf's theorem      95 98
Infinity-independent sequence      147

Integrable operator      4 5 9
Invariant (of an operator)      20—23 25—28 36 43—45 48 50 55 58 62 64 67 68 70 78 84 101 111 119 121 123 129 130 134 135 142 143 158 162 168—170 172 174 184 200 222
Jacobi function (elliptic)      91 117
Jacobi identity      4 43 63 197
Jordon extended basis      23 24
Jordon operator      23 33 87 128 129 134
Jordon,basis      27 29 31—33 132
Langer problem      122 166 173
Langer transformation      163
Larmor circle      61
Larmor local radius      61
Larmor radius      61
Lie algebra      197 199
Liouville’s equation      198
Longitudinal motion      65
Lyapunov coefficients      111
Lyapunov function      110
Lyapunov problem      105
Lyapunov stability condition      37 109 111
Lyapunov system      111
Lyapunov values      97
Lyapunov — Schmidt reduction      83
Matching domain      147 148 152 155 192
Matching problem      143 146—149
Maximal height      8 133 172
Minimal height      8 9 32 35 135 173
Model equation method      227
Newton polygon method      96
Nilpotent operator      8 10 13 29 31 33—35 77 105 127—129 131 134 135 138 172 173 176
Non-integrable operator      4 9 132 134
Nonperturbed system      118—120
Normal basis      29—32 34 105 106 111 133
Normal form (of a system)      76—79 81—83 85 95 207—209 226 244
Normal form (of an operator)      6 7 9—11 13 27 35 43—44 77 79 81 84 87 97 101 121 123 127—131 134—136 140 143 145 146 149 151 158 160 164 166 172—177 179 182 184 201 223
Permutability of two operators      4 5 7 168
Perturbation operator      10 11 134 162
Perturbed system      118 120
Point of resonance (i-point of resonance,i-point)      78—86 90 92—95 115 120 123 129 160 171
Poisson bracket of two functions      43 92
Principal part (of the perturbation)      128 137 174 176 234
Quasidiagonal operator      4
Quasilinear operator      23 28 121
Reconstructed operator      121 123 136—138 141—146 157 163 182 231
Reduction of information      40—43
Regularity condition      73
Riccati equation      182
Schroedinger equation      233 244
Schroedinger perturbation theory      27
Shearing transformation      11 29 33—35 105 107 113 127 128 134 135 139 162 174 177
Spectrum,complete degenerate      6 13
Spectrum,discrete      102 105
Spectrum,partially degenerate      6
Spectrum,simple      6
Standard summands      34
Transitional curve      85—87 96
Unbounded in height      4—5
Van der Pol equations      178
Weight (of an operator)      11 34—35 128 135 138 201-202

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