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Gröbner W., Knapp H, — Contributions to the method of Lie series
Gröbner W., Knapp H, — Contributions to the method of Lie series

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Название: Contributions to the method of Lie series

Авторы: Gröbner W., Knapp H,

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1967

Количество страниц: 277

Добавлена в каталог: 28.03.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Adaptation      59 60
Algebraic inequalities in the coefficients      115 116 132 133
Analytic continuation      23 65ff.
Approximation solutions      44 58 59 74 79 92
Bendixson      154
boundary conditions      67 71 92
Boundary conditions, value problems      67ff. 80
Boundary conditions, value problems, generalized      71ff.
Calculation, numerical      62
Calculation, of the integrals      64
CAUCHY's majorant method      3 226
CAUCHY's majorant method, problem for partial differential equations      232ff.
Celestial mechanics      73ff.
Characteristic vectors      104
Characteristics      101 102 106—110 121 164 214
Common invariants      163
Commutation* theorem      13 17 100
Complete systems      159
Computation      60
Computation, results      83 94
Continuation      see “Analytic continuation”
Convergence, domain of      46
Convergence, of extended invariant functions      156—158
Convergence, of generalized Lie series      222ff. 229
Convergence, of iteration      54
Convergence, of the Lie series      6ff. 10 13 140
Correction, of initial values      69 73
Critical point      100 154
Critical straight line      138
Decomposition of an operator      see “Split-up”
Degenerate cases      124
derivatives      49
Differential equations, ordinary      20 32ff 44 100
Differential equations, ordinary, homogeneous      118ff.
Differential equations, ordinary, linear homogeneous      104
Differential equations, ordinary, of the n-th order      60
Differential equations, ordinary, qualitative discussion      111 143 151
Differential equations, ordinary, qualitative discussion, figures      114 117 134 135 152
Differential equations, ordinary, solution formulas      35
Differential equations, ordinary, solution with respect to a parameter      39
Differential equations, ordinary, stability      111 212ff.
Differential equations, ordinary, van der Pol's      68 90ff.
Differential equations, partial      159ff. 180ff.
Differential equations, partial, connection with Duhamel integral      251ff.
Differential equations, partial, inhomogeneous      244ff.
Differential equations, partial, of higher order, Cauchy's problem      232ff.
Direction of rotation      123
Duhamel integral method      246 251ff.
Eigenvalue problem      70
Eigenvalue, of invariant chain      103
Eigenvalue, of invariant function      101
Error      30 57 62ff. 63 70
Error, propagation      65ff.
figures      114 117 134 135 152
Formal power series      155
Generalized Lie series      222ff.
Hamilton — Jacobi theory      196ff.
Hamilton — Jacobi theory, partial differential equation      199ff.
Hamilton — Jacobi theory, partial differential equation, complete solution      201
Holmgren's theorem      236
Holomorphic coefficients      154
Initial value problem      44
Invariant chain      102 105 113
Invariant chain, eigenvalue of      103
Invariant function      101 104 107—110 118 121 214
Invariant function, common      163
Invariant function, complex      102 105 112
Invariant function, eigenvalue of      101
Invariant function, real      102 105 112
Invariant straight line      137ff.
Involution      191
Iteration rule      52 53 61
Iteration rule, method ${G}_{m}$      52 53 54
Jacobian      47 66 68 72 81 94
Jacobian system      161
Jordan case      165
Jordan chains      104
Kepler      78 89
KOWALEVSKY, J.      73
KROGDAHL, W.      94
Leitmatrizen      69
Liapunov function      219
Lie ring      192
Lie series, as solutions of ordinary differential equations      20 32ff.
Lie series, definition      2
Lie series, generalized      222ff.
Lie series, generalized, applications      230
Limit cycle      91
Lipschitz condition      54
Loop sectors      124
MAESS, G.      94
Majorant, functions      2ff.156
Majorant, method      3 226
Majorant, operator      2ff.226
Mathieu's differential equation      70
n-body problem      74ff
Neighborhood, of a critical point      100 154
Neighborhood, of an invariant straight line      136
Newton      64 68 74 6u
Node sectors      124
Numerical calculation      62
Numerical calculation of the integrals      64
Numerical results      83 94
Operator      2ff.
Operator, of higher order      222ff.
Operator, simultaneous      159ff.189ff.
Operator, split-up of      34 45 52 59 75 77 93
Orbit, approximation      76 79
Orbit, of the moon      79
Orbit, of the sun      78
Ordinary differential equations      see “Differential equations”
Parameter expansion      37
Partial differential equation      see “Differential equations”
Periodic solutions      71 90 91
Perturbation theory      34ff»
Picard      154
PICARD, successive substitution      54
Poincare      36 39 154
Projection      149
Propagation of errors      65ff.
Qualitative, behavior      114 117 134 135 152
Qualitative, discussion      104 111ff. 123ff. 126 143 151
Rearrangement of Lie series      37 39 136
Remainder, of iteration rule      57 63
Remainder, of Lie series      26ff. 29 52
Rotation, direction of      123
Saddle sectors      124
sectors      123ff.
Sectors, node, saddle, loop      124
Solution formulas      35 45 48
Solution formulas, with respect to a parameter      39
Split-up of operators      34 45 52 59 75 77 93
Stability      111 2l2ff.
Stability of sectors      126
Step size control      64
Strip      187
Strip condition      184 187
successive substitution      54
Systems, of linear partial diff.eq. of, 1st order      156ff.
Systems, simultaneous      189
Theorem of commutation      13 17
Three body problem      73ff. 76ff.
Truncation errors      62ff.
Uebertxagungsmatrizen      69
Urabe, M.      94
Van der Pol's differential equation      68 90ff.
Vector notation      47
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