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| Blaszak M. — Multi-Hamiltonian Theory of Dynamical Systems |
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| Предметный указатель |
Action variable 7
Adiabatic approximation 131
Adjoint action 254
Adjoint Lax eigenfunction 278
Adjoint mapping 253
Adjoint R-martix 259
Adjoint representatives 18
Adjoint symmetry 57
Adler map 284
AKNS, constrained isospectral problem 168
AKNS, Hamiltonian representation 292
AKNS, hierachy 279
AKNS, Lax hierarchy 95
AKNS, system 61
AKNS, zero courvature hierarchy 100
AKNS,(2+1)-dimensional 323 325
Algebra, dual 255
Algebra, exterior 30
Algebra, fundamental 111
Algebra, general 79
Algebra, Hamiltonian 80
Algebra, hereditary 73 105
Algebra, Lax isospectral 104
Algebra, Lie 42 43 45 46 252
Algebra, non-canonical action/angle 113
Algebra, noncanonical action/angle 79
Algebra, operator 327
Algebra, pseudo-differential operators 264 326
Algebra, shift operators 293
Algebra, Virasoro 73
Angle variable 7
Bargmann constraint 167
Basis 15
Benjamin — Ono equation 80
bi-Hamiltonian, chain 71 195
bi-Hamiltonian, systems 52 184 328
bi-Hamiltonian, vector field 49 242
Bi-vector 43
Boussinesq equation 272 286
Bracket, Lie 42 252 257
Bracket, Lie — Poisson 256
Bracket, Poisson 137
Bracket, Schouten 31
Burgers equation 272
Calogero — Moser system 245
Canonical, action/angle variables 7 110
Canonical, coordinates 5
Canonical, Poisson matrix 5
Canonical, representation 5
Casimir function 6 138 262
Characteristic operator equation 92
Closed k-form 28
Co-adjoint action 255
Compatible structures 65
Completely integrable 7
Conserved quantity 52
Constrained AKNS isospectral problem 168
Constrained DWW isospectral problem 167
Constrained MKdV isospectral problem 172
Constrained Schroedinger spectral problem 166
Constrained system 136
Constraint, Bargmann 167
Constraint, Kupershmidt 276
Contraction 15
Cosymmetry 57
Cotangent bundle 16
Covector fields 16
Davey — Stewardson equation 323
Derivative 18 21
Derivative, directional 23 27
Derivative, dual 19 21
Derivative, exterior 28 38
Derivative, Gateaux 91
Derivative, Lie 34 38
Derivative, total 25
Derivative, variational 81
Dirac reduction 263 284 287
Directional derivative 23 27
Dispersive water waves equation 50
Dressed operator 320
Dressing operator 319
Dual algebra 255
Dual derivative 19 21
Duality map 13 17 255
Dynamical system 1
Equation, AKNS 61
Equation, Benjamin — Ono 80
Equation, Boussinesq 272
Equation, Burgers 272
Equation, Calogero — Moser 245
Equation, cylindrical Korteweg-de Vries 62
Equation, Davey — Stewardson 323
Equation, dispersve water waves 50
Equation, Euler 6
Equation, field Gamier 236
Equation, Garnier 166 169
Equation, Hamilton — Jacobi 191 206
Equation, Harry-Dym 50
Equation, Henon — Heiles 4 143 185 200
Equation, Ishimori 324
Equation, Kadomtsev — Petviashvili 82 321 332
Equation, Kaup — Kupershmidt 276
Equation, KdV with sources 233
Equation, Kepler 215
Equation, Korteweg-de Vries 3 49 60 68 77 268
Equation, Melnikov 239
Equation, modified Boussinesq 273
Equation, modified dispersive water wave 84
Equation, modified Kadomtsev — Petviashvili 84 322
Equation, modified Korteweg-de Vries 49 61
Equation, modified Yang — Baxter 261
Equation, Neumann 167 220
Equation, Novikov — Veselov 333
Equation, relativistic Toda 311
Equation, Sawada — Kotera 61 277
Equation, Toda 3 62 243 295
Equation, Yang — Baxter 258
Euler equation 6
Evolution parameter 33
Exact k-form 28
Extended noninteracting particles 120
Extended phase space 138
Exterior derivative 28 38
Exterior product 30
Flow 2 32 54
Flow, constrained 166
Flow, isospectral 89
Flow, N-soliton 130
Flow, perturbed 131
Flow, restricted 177
Flow, stationary 137
Fundamental algebra 111
Garnier system 166 169
Gateaux derivative 91
Gelfand — Dikii spectral problem 283
General algebra 79
Gradient 23
Group Lie 250
Group of diffeomorphisms 32
Hamilton — Jacobi equation 191 206
Hamiltonian action/angle vector field 114
Hamiltonian algebra 80
Hamiltonian dynamical system 49
Hamiltonian formalism 5
Hamiltonian function 49
Hamiltonian vector field 49
Harry-Dym equation 50
Henon — Heiles system 143 185 200
Hereditary algebra 73 105
Hereditary operator 63
| Hierarchy, elliptic separable potentials 208
Hierarchy, Harry-Dym-(2+1) 318
Hierarchy, Kadomtsev — Petviashvili 314
Hierarchy, matrix KP 322
Hierarchy, matrix modified KP 323
Hierarchy, modified Kadomtsev — Petviashvili 316
Hierarchy, Novikov — Veselov 332
Hierarchy, parabolic separable potentials 212
Hilbert transform 80
Implectic manifold 43
Implectic operator 43
Infinitesimal generator 32
Integral curve 1
Integrating factor 185
Interacting soliton 107
Interior product 27 38
Inverse Hamiltonian vector field 49
Inverse Pfaffian vector field 189
Ishimori equation 324
Isospectral deformation 2
Jacobi identity 18
Kadomtsev — Petviashvili equation 82 321 332
Kaup — Kupershmidt equation 276
KdV Lax hierarchy 94
Kepler problem 215
Kernel representation 335
Korteweg-de Vries equation 3 49 60 68 77 268
Kupershmidt constraint 276
Kupershmidt reduction 276
Lax, adjoint eigenfunction 278
Lax, dynamics 249
Lax, eigenfunction 278
Lax, hierarchies 266
Lax, isospectral equation 2
Lax, nonisospectral equation 91
Lax, operator 88
Lax, pair 2
Left action 252
Left invariant 251
Left translation 250
Legendre transformation 137
Leibniz rule 264
Levi-Civita condition 191
Lie, algebra 18 42 43 45 46 252
Lie, bracket 42 43 252 257
Lie, derivative 34 38
Lie, group 250
Lie, symmetry 55
Lie, transport 33
Linear system 109
Linear topological space 1
Manifold, bi-Poisson 64
Manifold, Poisson — Nijenhuis 65 241
Manifold, Riemannian 217
Master symmetries 78
Master tensor invariant 76
Melnikov system 239
Miura map 84
Modified Boussinesq equation 273 289
Modified dispersive water wave equation 84
Modified Gamier equation 175
Modified hierarchies 309
Modified Kadomtsev — Petviashvili equation 84 322
Modified KdV equation 49 61
Modified KdV with sources 235
Modified Yang — Baxter equation 261
multi-Hamiltonian vector fields 67
multi-vectors 30
Neumann equation 220
Neumann system 167
Newton representation 152
Newton stationary Harry-Dym 164
Newton stationary KdV 158
Nijenhuis, chain 195
Nijenhuis, coordinates 189
Nijenhuis, operator 63
Nijenhuis, torsion 64
Non-Hamiltonian symmetries 74 113
Nonisospectral problem 91
Nonisospectral zero-curvature equation 91
Nonlinear Schroedinger equation 50
Nonstandard Hamiltonian structure 220
Nonstandard Hamiltonian structure, DWW 229
Nonstandard Hamiltonian structure, field Gamier 236
Nonstandard Hamiltonian structure, KdV 224
Nonstandard Hamiltonian structure, Melnikov system 239
Novikov — Veselov equation 333
Operand 327
Operator, algebra 327
Operator, dressed 320
Operator, dressing 319
Operator, hereditary 63
Operator, implectic 43
Operator, Lax 88
Operator, Lax isospectral 101
Operator, Lax nonisospectral 101
Operator, normal form 138
Operator, Poisson 43
Operator, recursion 59
Operator, regular 138
Operator, symplectic 45
Operator, undressed 319
Operator, variational 24
Orbit 253
Ostrogradsky representation 137
Perturbed flow 131
Pfaffian vector field 189
Poincare lemma 28
Poisson bracket 43 137
Poisson manifold 43
Poisson operator 43
Poisson pencil 64
Pull-back 19
Push-forward 18
quasi-bi-Hamiltonian 185
R-matrix 249
R-structure 257
Reciprocal transformation 281
Recursion operator 59
Regular operator 138
Relativistic Toda lattice 311
Restricted flow 177
Restricted Harry-Dym 177
Restricted KdV 177 182
Riemannian manifold 217
Right action 252
Right invariant 251
Right translation 250
Sato equation 320
Sato theory 313
Sawada — Kotera equation 61 277
Scalar field 19
Schouten bracket 31
Separability 184
Separability elliptic potentials 208
Separability Garnier system 211
Separability Kepler equation 215
Separability spherically symmetric potentials 216
Separability stationary Harry-Dym 201
Separability stationary KdV 202
Separable system 191
Soliton, Hamiltonian vector fields 119
Soliton, particle 107 122
Soliton, perturbation theory 130
Soliton, solution 107
Staeckel space 218
Staeckel system 218
Stationary, DWW 141 145 149
Stationary, flow 137
Stationary, Harry-Dym 140 145 148
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