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Ilyashenko Yu., Yakovenko S. — Lectures on analytic differential equations |
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Предметный указатель |
#M the number of isolated points in an analytic set M 191
functions holomorphic in U and continuous in the closure 3
formal isomorphisms of Cn at the origin 24
vector fields holomorphic in U 8
formal vector fields in at the origin, infinite jets of vector fields 24
Apparent singularity 266
Bautin depth 183
Bautin ideal 183 186 197
Bautin ideal, iterated 187
Bautin index 183
Bernstein classes 195
Birkhoff — Grothendieck cocycle 240
Birkhoff — Grothendieck cocycle, standard 244 245
Birkhoff — Grothendieck covering 240
Blow-up 93
Blow-up of analytic curve 95
Blow-up of singular foliation 96
Blow-up, blow-down 93
Blow-up, simple 95
Bolibruch — Kostov theorem 266
Bundle, determinant 277 287
Bundle, equivalence 278
Bundle, map 278
Bundle, normal 120
Bundle, section 278
Bundle, trivial 278
Bundle, vector 277
C(U) functions continuous in U 3
Capacity 57 60
Cartan cocycle 240
Cartan covering 240
Center–focus alternative 151
Characteristic matrix 236 237
Cocycle, asymptotically trivial 258 324
Cocycle, matrix cocycle 238
Cofactor 211
Cone 71
Connection, trace 288
Corner point 133
Covering, convenient 322
Cyclicity 181
Cyclicity, complex 191
Decidable set, property 143
Degree of line bundle 285
Degree of meromorphic section 285
Degree of vector bundle 287
Derivation-division process 192
Determinant of vector bundle 287
Divisor 100
Divisor, exceptional 93
Divisor, preimage by a holomorphic map 102
Elliptic singularity 152
Elliptic singularity, integrable 164
Equivalence of linear systems, global meromorphic 225
Equivalence of linear systems, local holomorphic 226
Equivalence of linear systems, local meromorphic 226
Euler system 225
First integral 164
Flat function 314 319
Flip 145
Formal equivalence, ramified 318
Formal flow 26
Formal map 24
Fundamental matrix solution 217
Fundamental system of solutions of linear system 218
Gauge equivalence 219
Generalized elliptic singularity (point) 151 152
Holomorphic foliation, singular 19
Holonomy map, group 17
Holonomy operator 224
Homological equation 327
| Hyperbolicity, complex 71
Index of a complex separatrix 117
Integrable germ, group 171
Integrable singularity, elliptic 164
Intersection, isolated 103
Leading matrix 314 316
Levelt form 235
Line field 14
Linearization form 117
Matrix cochain 238
Matrix exponent 222
Matrix logarithm 28
Moderate growth condition 227
Monodromy group 223
Monodromy group, irreducible 266
Monodromy operator 222
monopole 246
Monopole group 247
Non-dicritical singularity 99
Normalizing cochain 322
Operator of monodromy 222
Operator, irreducible 302
Orbital equivalence, holomorphic 19
Orbital equivalence, topological 20
Order of germ 106
Order of singularity 98
Partial index 245
Periodicity alternative 145
Pfaffian matrix 216
Plemelj theorem 265
Poincar?e rank 226 314
Poincare — Dulac — Levelt normal form 235
Ray, exceptional 314
Ray, separating 319
Resonance for Fuchsian singularities 231
Resonance for irregular singularities 316
Resonant monomial 231
Resonant normal form for Fuchsian singularities 235
Resonant normal form of Fuchsian singularities 231
Resonant subspace 235
Riemann — Hilbert problem 260
Rigidity 78
Rohrl — Plemelj theorem 264
Saturation 168 175
Sector 320
Sector of fall 314 329
Sector of growth 314 329
Sector, acute 326
Semi-monodromy 153
Semialgebraic set 135
Semiformal series 182
Separatrix 99 116
Series, semiformal 182
Singularity of linear system 226
Singularity, apparent 266
Singularity, elementary 97
Singularity, Fuchsian 229 282
Singularity, logarithmic 282
Singularity, regular, for linear system 227
Solution, formal 26
Stokes collection 322
Strongly contracting operator 52
Sufficient jet 136
Tangency point 97 98 100
Tangent form 99
Topological orbital equivalence 20
Trace of connection 288
Trace of foliation 70
Transition time 81
Unipotent operator 25
Variation of constants 221
Vertical function 319
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