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Ilyashenko Yu., Yakovenko S. — Lectures on analytic differential equations
Ilyashenko Yu., Yakovenko S. — Lectures on analytic differential equations

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Название: Lectures on analytic differential equations

Авторы: Ilyashenko Yu., Yakovenko S.

Язык: en

Рубрика: Математика/Анализ/Комплексный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 344

Добавлена в каталог: 02.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
#M the number of isolated points in an analytic set M      191
$A(U) = \mathcal{O}(U) \cup C(\bar{U})$ functions holomorphic in U and continuous in the closure      3
$Diff[[\mathbb{C}^n,0]]$ formal isomorphisms of Cn at the origin      24
$\mathcal{D}(U)$ vector fields holomorphic in U      8
$\mathcal{D}[\mathbb{C}^n,0]$ formal vector fields in $\mathbb{C}^n$ 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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