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| van der Meer J.-C. — The Hamiltonian Hopf Bifurcation |
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| Предметный указатель |
 -determined map 51
 -normal form 32—33
Abraham, R. 4 8 11
Action integral 87
Action-angle coordinates 14 83
Ad*-equivariant 11
Adjoint representation 8
Anti-symplectic reflection 69
Arnold, V.I. 4 8 11 13 17 53
Bierstone, E. 46 47 51
Birkhoff generator 35
Birkhoff, G.D. 34 44 102
Borel 20
Bouquet 43
Briot 43
Brjuno, A.D. 20 43 45
Broer, H.W 24 43
Brown, E.W. 100
Buchanan, D. 100
Burgoyne, N. 16 43 98 101
Canonical coordinates 6
Canonical map 6
Caprino, S. 102
Chen, K.T. 24 27 43 44
Cherry, T.M. 44
Churchill, R.C. 68
Closed two-form 5
Co-adjoint action 11
Co-dimension of a map 51
Collinear equilibrium point 97
Complete vector field 13
Complex conjugate variables 33
Critical mass ratio of Routh 97
Cushman, R.H. 16 43 45 68 69 83 98 101
D'Onofrio, B. 102
Darboux's theorem 5 20
Deformation of a map 52
Deformation of an Hamiltonian normal form 85
delaunay 44
Dell'Antonio, G.F. 39 102
Deprit, A. 44 45 97 100
Dugas, R. 9
Duistermaat, J.J. 39 56 65 83 84
Dulac, M.H. 43
Eigenvalues of infinitesimal symplectic maps 15
Eliasson, H. 42
Energy-momentum mapping 10
Equilateral equilibrium point 97
Equivalent Hamiltonian functions 55
Equivalent Hamiltonian systems 55
Equivalent maps 49
Equivariant map 48
Euler equilibrium point 97
Euler, E. 97 98 99 102
Finitely determined map 51
Flow of a vector field 6
Formal power series 20
Functions in involution 13
Galgani, L. 45
General problem of three bodies 96
GENERIC 93
Giorgilli, A. 45
Gustavson, F.G. 44
Gylden 99
Hamiltonian function 4 5
Hamiltonian Hopf bifurcation 18
Hamiltonian system 5
Hamiltonian system of differential equations 5
Hamiltonian vector field 5
hilbert 48
Hilbert generators 48
Hilbert map 48
Hilbert's theorem 48
Homoclinic orbit 93—94
Homogeneous polynomial 20
Humphreys, J.E. 23
Independent integrals 13
Infinitesimal generator 10
Infinitesimal stability 50
Infinitesimal symplectic map 14
Infinitesimal symplectic matrix 15
Inner derivation 8
Integrable Hamiltonian system 13
integral 7
Integral curve 6
Invariant map 47
Invariant torus 93—94
Izumya, S. 46 47
Jacobi identity 7
Jacobi, C.G.J. 99
Jacobian module 50
Jacobson — Morosov lemma 32
Jacobson, N. 32
jet 20
Jordan decomposition 17
Jordan — Chevalley decomposition 22
Kelley, A. 43
Kummer, M. 68
Lagrange equilibrium point 92
Lagrange, J. 97 99
Lasalle, M.G. 92
| Liapunov, A. 43
Liapunov-stable (unstable) 83
Lie algebra 7
Lie bracket 8
Lie series 9
Linear Hamiltonian system 14ff
Linearized system 18
Maffei, C. 102
Marsden, J.E. 4 8 11
Martinet, J. 47
Mather, J.N. 47
Maximal ideal 49
Maximal integral curve 6
Mementum mapping 10
Meyer, K.R. 44 45 101 102
monodromy 83
Monomial 34
Moser — Weinstein reduction 84ff
Moser, J. 34 44 45 84
Negrini, P. 102
Nilpotent formal power series 26
Nondegenerate two-form 5
Nonresonant system 34
Nonsemisimple resonance 16
Normal form algorithm 25
Normal form for energy-momentum mappings 46
Normal form for Hamiltonian systems 19ff
Normal form for linear Hamiltonian systems 16
One-parameter group 6 10
One-parameter symmetry group 11
Orbit of  in  29
Orbit of an Hamiltonian vector field 6
Orbit space 67
Pedersen, P. 100
Phase portrait 6
Poenaru, V. 46 47 48 50 51
Poeschel, J. 94
Poincare, H. 43 99
Poisson bracket 7
Poston, T. 78
Pull-back 6
Reduced Hamiltonian function 12 68
Reduced Hamiltonian system 12
Reduced phase space 12 68
Reduced potential 70
Reduction 68
Reduction Theorem 11
Relative equilibrium 12
Resonance 16 18 39
Resonance generator 35
Resonant Hamiltonian system 16 18 35
Restricted problem of three bodies 95ff
Right-action 46
Right-left action 46
Right-left equivalence 49
Roberts, M. 46 47
Robinson, R.C. 94
Rod, D.L. 68 69
Roels, J. 101
Routh, E.J. 100
S-equivariant map 48
S-equivariant vector field 48
S-invariant function 47
S-invariant map 48
S-N decomposition 22
S-normal form 23ff
Schmidt, D. 45 101
Schwartz, G. 48
Semisimple formal power series 26
Siegel, C.L. 20 43 44 45
Smale, S. 55 66
Smooth vector field along a map 50
Space of periodic curves 86
Stable map 49
Standard function 56
Sternberg, S. 26 43
Stewart, I.N. 78
Swallowtail surface 78
Sweet, D. 101
Symmetry group 10
Symplectic action 10
Symplectic chart 6
Symplectic coordinates 6
Symplectic form 5
Symplectic group 14
Symplectic manifold 5
Symplectic map 6
Symplectic matrix 15
Symplectic vector space 8
Szebehely, V. 95 99
Takens, F. 24 43
Trivial action 48
Universal deformation 52
van der Meer, J.C. 17 24 45 57 98
Vegter, G. 92
Versal deformation 16
Volk, O. 98 99
Wassermann, G. 47 50
Weinstein, A. 84
Whittaker, E.T. 43
Williamson, J. 43
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