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