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Cohen A. — Introduction to the Lie theory of one-parameter groups
Cohen A. — Introduction to the Lie theory of one-parameter groups



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Название: Introduction to the Lie theory of one-parameter groups

Автор: Cohen A.

Аннотация:

The object of this book is to present in an elementary manner, in English, an introduction to Lie's theory of one-parameter groups, with special reference to its application to the solution of differential equations invariant under such groups.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1911

Количество страниц: 248

Добавлена в каталог: 06.12.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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