Birkhoff normal form 125 144
Canonical coordinate system 124 144
Coboundary homomorphism 78
Cohomologic interpretation 37 80
Conjugate, linear operators 93
Conjugate, surfaces 263
Cycle of a mapping 182
Cycle of a vectorfield (a phase flow) 160
Cycle, length of 182
Cycle, symmetric 159 184
Cycle, symmetric, long period 255 282
Cycle, symmetric, short period 255 282
Cycle, symmetric, very long period 202
Diagrams, equivalent 16
Diagrams, standard 17
Diffeomorphism (mapping), cycle of 182
Diffeomorphism (mapping), elliptic 102
Diffeomorphism (mapping), elliptic hyperbolic 110
Diffeomorphism (mapping), hyperbolic 112
Diffeomorphism (mapping), integrable 1 23
Diffeomorphism (mapping), nondegenerate 23 148
Diffeomorphism (mapping), pseudoreversible 297
Diffeomorphism (mapping), reversible 5
Diffeomorphism (mapping), slightly elliptic 102
Diffeomorphism (mapping), slightly integrable 23
Diffeomorphism (mapping), symmetric cycle of 184
Diffeomorphism (mapping), symmetric trajectory of 193
Diffeomorphism (mapping), trajectory of 193
Diffeomorphism (mapping), weakly pseudoreversible 298
Diffeomorphism (mapping), weakly reversible 1 5
Double, conjugation 111
Double, numbers 111
Double, numbers, exponent of 140
Dynamical system with continuous time 66
Dynamical system with discrete time 4 22
Dynamical system, reversible 2 5
Dynamical system, reversible, in the generalized sense 300
Dynamical system, weakly reversible 5
Equivariant, function 199 219
Equivariant, vectorfield 200 220 227
Focus exponential 212
Generalized Jordan block 95
Homological equations 34 75
Homotopic method 249
Independence, functional 109
Independence, rational 3
Intersection property 2 57 154
Involution 2
Involution of type (p, q) 92
Isotropic plane 268
Kolmogorov torus 4
Limiting degeneration 182
Linear operator, infinitesimally reversible 93
Linear operator, reversible 93
Linearization 92
Lyapunov theorem 223
Lyapunov — Devaney theorem 230
Matrix, infinitesimally symplectic 94
Matrix, symplectic 93
| Middle dimension 6
Monodromy operator 173
Monomial antiresonant 114 137 138
Monomial resonant 113 114 137 138
Non-autonomous differential equation, quasireversible 171
Non-autonomous differential equation, reversible 172
Non-autonomous differential equation, symmetric periodic solution of 175
Non-autonomous differential equation, T-periodic 172
Non-autonomous differential equation, weakly reversible 172
Normal function 2 0
Phase oscillations 12 194
Phase oscillations, equations of 201
Poincare mapping, complete 160
Poincare mapping, semi- 160
Poincare — Dulac theorem 115 138
Poisson brackets 74
Proper degeneracy 7
Regime (elliptic and hyperbolic) 236 237 255 256 282 283
Resonance 14 104 133 221 228 230 235 282
Resonance (resonant) zone 11
Resonance (resonant) zone, local theory of 221
Resonance (resonant) zone, width of 200 219 227
Resonance of codimension one 235 282
Resonance, higher 254
Resonance, order of 104 126 133 145
Resonance, strict 235 282
Resonance, strong 227
Resonance, subharmonic 282
Resonance, weak 221
Return, curve 15
Return, function 160
Return, surface 16
Rotation numbers 165
Saddle with zero trace 158 211
Saddle, exponential 213
Similar matrices 93
Singularity of type  16 262 268 276
Situation, elliptic 164
Situation, slightly elliptic 164
Small denominator condition 22 66 182
Twist rotation 1 56
Type of a number in  22 66
Type of a surface 263
Type of an involution 92
Vectorfield (or autonomous differential equation), cycle of 160
Vectorfield (or autonomous differential equation), elliptic 102
Vectorfield (or autonomous differential equation), elliptic hyperbolic 136
Vectorfield (or autonomous differential equation), hyperbolic 137
Vectorfield (or autonomous differential equation), integrable 3 68
Vectorfield (or autonomous differential equation), nondegenerate 3 60 157
Vectorfield (or autonomous differential equation), pseudoreversible 2 98
Vectorfield (or autonomous differential equation), reversible 2
Vectorfield (or autonomous differential equation), slightly elliptic 102
Vectorfield (or autonomous differential equation), slightly integrable 68
Vectorfield (or autonomous differential equation), symmetric cycle of 159
Vectorfield (or autonomous differential equation), symmetric trajectory of 159
Vectorfield (or autonomous differential equation), weakly pseudoreversible 298
Vectorfield (or autonomous differential equation), weakly reversible 5
Whitney, mapping 248
Whitney, umbrella 16 248
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