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| Birkhoff G.D. — Dynamical Systems |
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| Ïðåäìåòíûé óêàçàòåëü |
Analyticity of solutions 12—14
Ascoli 4
Asymptotic motion to periodic motions 211—212 227—237
Asymptotic motion to recurrent motions 205—206
Billiard ball problem 169-79
Billiard ball problem for ellipse 248—255
BLISS 1
Bohr 220
Bolza 35 37
Brouwer 148 234
Cantor, G. 194
Central motions 190—197 202—204
Central motions, special 202—204
Central motions, transitivity and intransitivity of 205—208
Characteristic surface 129
Chazy 260
Clausius iii
Closed geodesics 130 135—139
Closed geodesics on a special closed surface 244—245
Closed geodesics on convex surfaces 135—139
Closed geodesics on open surfaces 132—134
Closed geodesics on symmetric surfaces 130—132
Conservation of energy 14—19
Conservative systems 14—19
Conservative systems, change of variables 19—21
Conservative systems, subject to constraints 22
Contact transformations 53—55
Continuity theorems 6—10 10—12
coordinates 14—15
Cosserat, E. and F. 14
Degrees of freedom 14
Dissipative systems 31—32
Energy 23—25
Equations of variation 10 57—58
Equilibrium problem 59 60 67—71
Equilibrium problem, Hamiltonian case of 74—85
Equilibrium problem, Pfaffian case of 89—94
EQUIVALENCE 56
Euler 35
Existence theorem 1—5 10—12
External forces 14—15
Formal group 60—63
Formal solutions 63—67
Formal solutions, containing a parameter 143
Galileo iii
Generalized equilibrium 60
Generalized equilibrium, Hamiltonian case of 85—89
Generalized equilibrium, normal form for 71—74
Generalized equilibrium, Pfaffian case of 94—96
Generalized equilibrium, reduction to 97—100
Geodesics 38—39 180—188
Geodesics in a transitive case 238—248
Geodesics in an integrable case 248—255 (see also “Closed geodesies”)
Goursat 1
hadamard iv 128 130 170 211 238
Hamilton iii
Hamiltonian principal function 52
Hamiltonian systems 50—53
Hamiltonian systems, Lagrangian and 50—53
Hamiltonian systems, normal forms of 74—85 85—89
Hamiltonian systems, transformations of 53—55
Hamilton’s principle 34—36
hilbert 130
Hill iii 139 260
Ignorable coordinates 40—44
Index of invariant point 176
Instability 105 220—231
Instability, zones of 221—226
Integrability 255—259
Integral of energy 18 52
Integral of energy in the problem of three bodies 261—263
Integral of energy, conditional linear 45—47
Integral of energy, linear in velocities 44—45
Integral of energy, quadratic 48—50
jacobi iii 170 248
Koopman 145
Lagrange iii 263 264 278 285
Lagrangian systems 18—19
Lagrangian systems, external characterization of 25—31
Lagrangian systems, Hamiltonian and 50—53
Lagrangian systems, integrals of 41—50
Lagrangian systems, internal characterization of 23—25
Lagrangian systems, normal form of 39—40;
Lagrangian systems, reduction of order of 40—41
Lagrangian systems, regular 25
Lagrangian systems, transformation of 36—39
Laplace iii
Lebesgue 248
| Levi — Civita iv 270 273 275
Liapounoff 122
Liouville 48
Lipschitz 5
Manifold of states of motion 143
Manifold of states of motion in problem of three bodies 270—275 283—288
Mass 23
Morse 139 170 238 246 247
Multipliers 74
Multipliers, Hamiltonian 74—78;
Multipliers, Pfaffian 89—91
Newton iii
Non-energic systems 18
Osgood 4 138
Painleve 261
Particle 23—25
Particle in force field 124—128 146—149
Periodic motions 59
Periodic motions, analytic continuation of 139—143
Periodic motions, minimal type of 133—139
Periodic motions, minimum type of 128—132
Periodic motions, near a periodic motion 159—165
Periodic motions, near generalized equilibrium 150—154
Periodic motions, obtained by the transformation method 143—149
Periodic motions, role of 123—124;
Periodic motions, simple and multiple 142
Periodic motions, stable and unstable 209—215
Pfaffian systems 55
Pfaffian systems, generalized equilibrium of 97—100
Pfaffian systems, instability of 105
Pfaffian systems, multipliers of 89—91
Pfaffian systems, normal form of 91—96
Pfaffian systems, stability of 100—104
Pfaffian systems, variational principle for 55
Picard 1 13 105 122
Poinca.e iii 74 97 105 123 139 143 190 194 223 237 255 257 260 288
Poincare’s geometric theorem 165—169
Poincare’s geometric theorem, application of 150—88
Principal function of conservative systems 17
Principle of least action 36—39
Principle of reciprocity 26
Problem of three bodies 260—261
Problem of three bodies, collision in 267—270
Problem of three bodies, equations of 261—262
Problem of three bodies, generalization of 291—292 (see also “Restricted Problem of Three Bodies”)
Problem of three bodies, integrals of 262—263
Problem of three bodies, Lagrange’s equality in 264—265;
Problem of three bodies, manifold of states of motion in 270—275 283—288;
Problem of three bodies, properties of motions of 275—283 288—291
Problem of three bodies, reduction of 263—264 283-284;
Problem of three bodies, Sundman’s inequality in 265—267;
Quasi-periodic motions 218—220
Rayleigh iii 26
Recurrent motions 198—201 204—205 223—224
Restricted problem of three bodies 145 171 260
Reversibility 27 115
Reversibility and stability 115—121
Rotation number 184
Signorini 130
Solution 2
Stability 97—122
Stability of Hamiltoman and Pfaffian systems 97
Stability of Hamiltoman in case of two degrees of freedom 220—227
Stability of Hamiltoman in the sense of Poisson 174 190 197
Stability of Hamiltoman, complete 105—115
Stability of Hamiltoman, criterion of 226—227
Stability of Hamiltoman, permanent 121
Stability of Hamiltoman, problem of 121 227
Stability of Hamiltoman, reversibility and 115-120
Stability of Hamiltoman, unilateral 122;
State of motion 1
Surface of section 143—145
Surface of section, local 151—152
Suudman iv 260 261 265 270 278 283
Systems with one degree of freedom 19
Systems with two degrees of freedom 19
Systems with two degrees of freedom, integrals of 45—50
Systems with two degrees of freedom, motions of 150—185 209—255
Systems with two degrees of freedom, normal form for 39—40
Transitivity 205—208
Uniqueness theorems 5—6 10—12
Variational principles of dynamics 34—39 55—58
Variational principles, algebraic 33—34
Voss 14
Wandering motions 190—195
Weierstrass 261
Whittaker iv 25 55 89 130 132 162 170 248 284
Work 14
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