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| Авторизация |
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| Поиск по указателям |
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| Cohen A. — Introduction to the Lie theory of one-parameter groups |
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| Предметный указатель |
Affine tr. 3 54
Alternant 44
Alternant of symbols of extended trs. 209
Asymptotic lines 80
Bernoulli equation 58
Canonical form 26 34 64 155
Canonical variables 26 34 64 156
Change of variables 23 33 188
Characteristic function of infl. contact tr. 186
Classification of two-parameter grs. 152
Commutator 45
Complete system 104 106 110
Complete system, equivalent 106
Complete system, Jacobian 107 110
Contact infl. 185
Contact tr. 178 181
Curvature, lines of 81
Curve of union of elements 175 189
Dif. eq. of 2. ord. i. u. gr. 86 90 134 137 148 165 236
Dif. eq. of 2. ord. not i. u. any gr. 206
Dif. eq. of n. order i. u. gr. 99 101 236
Differential equation of 1. ord. 189
Differential equation of 1. ord. i. u. gr. 40 44 45 46 48 50 52 194 231
Differential invariant 51 88 194
Dilatations 185 186
Displacements 212
Distinct grs. 122 123 125
Distinct infl. trs. 7
Elements, lineal 175
Elements, lineal, union of 175 194
Equivalent complete systems 106
Essential parameters 214
Essential parameters, condition for 226
Extended gr. 42 84
Extended point tr. 41 83 180
First differential invariant 51 194
First integral 191
General expression for gr. leaving dif. eq. of 1. ord. unaltered 49
Group 1 28 211
Group of contact trs. 185
Group of infl, trs. 146
Group property 2
Group, distinct 122 123 125
Group, extended 42 84
Group, generated by infl. tr. 10 12 14 30 220
Group, involving one parameter 1 28
Group, involving r parameters 211
Group, trivial 39 119 196
Homogeneous dif. eq. (Boole) 93
Identical tr. 4
Independent linear partial dif. eqs. 104
Infinitesimal contact tr. 185
Infinitesimal contact tr., characteristic function of 186
Infinitesimal contact tr., symbol of 186
Infinitesimal tr. 6 29 197 215 218
Infinitesimal tr., distinct 7
Infinitesimal tr., gr. generated by 10 12 14 30 220
Infinitesimal tr., linearly independent 143 217
Infinitesimal tr., r-parameter gr. of 146
Infinitesimal tr., symbol of 8 42 84 85 218
Integrating factor 37 47 69 76
Integrating factor, common to two dif. eqs. 72
Integrating factor, two, for the same dif. eq. 48
Intermediary integral 191
Invariant 16 31
Invariant curve 17 18 31 32
Invariant dif. eq. see "Dif. eq."
Invariant differential 51 88 194
Invariant equation 18 32
Invariant family of curves 20 22
Invariant linear partial dif. eq. 115 118 119 122 124
Invariant point 17 19 31
Invariant surface 31 32
Inverse tr. 3 29 211
Involute 70
| Involute of a circle 70
Involution, functions in 179
Isothermal curves 72 79 203
Jacobi's identity 121
Jacobian complete system 107 110
Lie gr. 3
Lie's principal theorem 225
Lineal element 175
Linear ordinary dif. eq. of 1. ord. 56 57
Linear ordinary dif. eq. of 2. ord. 92 94 139 140 173 174
Linear ordinary dif. eq. of n. ord. 102
Linear partial dif. eq. i. u. a gr. 115 118 119
Linear partial dif. eq. i. u. two grs. 122 124
Linearly independent infl. trs. 143 217
Linearly independent infl. trs., number of, leaving dif. eq. of ord. n>2 unaltered limited 143 146
Lines of curvature 81
Method of solution of complete system 111 113
Method of solution of dif. eq. of 1. ord. 38 49 63 66 193
Method of solution of dif. eq. of 2. ord. 88 134 137 165 169 193
Method of solution of dif. eq. of n. ord. 101
Method of solution of linear partial dif. eq. 119 124
Minimal lines 78
n-times-extended gr. 84
n-times-extended tr. 83
Once-extended gr. 42
Once-extended tr. 41
Parallel curves 70
Path-curve 4 10 11 17 18 19 31 67
Perspective tr. 3
Point tr. 40
Point tr., extended 41 83 180
Poissonian symbol 179
Product of trs. 2
Projective tr., general 213
r-parameter gr. of infl. trs. 146
r-parameter gr. of trs. 211 214
Reciprocal polars, tr. by 180 184
Riccati equation 52 59 201
Rotations 2
Second differential invariant 88
Separation of variables 63
Similitudinous tr. 3
Singular solution 66
Subgroup 149
Symbol of extended infl. tr. 42 84 85
Symbol of infl. contact tr. 186
Symbol of infl. tr. 8 218
Transform of a tr. 24
Transformation by reciprocal polars 180 184
Transformation, affine 3 54
Transformation, contact 178 181
Transformation, extended 41 83
Transformation, general projective 213
Transformation, gr. of 1 28 211
Transformation, identical 4
Transformation, infl. 6 29 185 197 215 218
Transformation, inverse 3 29 211
Transformation, perspective 3
Transformation, point 40
Transformation, product of 2
Transformation, similitudinous 3
Translation 2 53 212
Trivial gr. 39 119 196
Twice-extended gr. 84
Twice-extended tr. 83
Two-parameter grs, classification of 152
Two-parameter subgroups always exist 150
Types of dif. eqs. of 1. ord. i. u. given grs. 52 231
Types of dif. eqs. of 2. ord. i. u. given grs. 90 236
Types of dif. eqs. of n. ord. i. u. given grs. 101 236
Union of elements 175 176 194
Union of elements, curve of 175 189
United elements 175
Variables, canonical 26 34 64 156
Variables, change of 23 33 188
Variables, separation of 63
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