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Zoladek H. — Monodromy Group
Zoladek H. — Monodromy Group



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Название: Monodromy Group

Автор: Zoladek H.

Аннотация:

In singularity theory and algebraic geometry the monodromy group is embodied in the Picard-Lefschetz formula and the Picard-Fuchs equations. It has applications in the weakened 16th Hilbert problem and in mixed Hodge structures. In the theory of systems of linear differential equations one has the Riemann-Hilbert problem, the Stokes phenomena and the hypergeometric functions with their multidimensional generalizations. In the theory of homomorphic foliations there appear the Ecalle-Voronin-Martinet-Ramis moduli. On the other hand, there is a deep connection of monodromy theory with Galois theory of differential equations and algebraic functions. All this is presented in this book, underlining the unifying role of the monodromy group.

The material is addressed to a wide audience, ranging from specialists in the theory of ordinary differential equations to algebraic geometers. The book contains a lot of results which are usually spread in many sources. Readers can quickly get introduced to modern and vital mathematical theories, such as singularity theory, analytic theory of ordinary differential equations, holomorphic foliations, Galois theory, and parts of algebraic geometry, without searching in vast literature.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 580

Добавлена в каталог: 22.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Structure, almost complex, integrable      336
Structure, complex      334
Structure, Hodge      196 224
Structure, Hodge, asymptotic mixed      251
Structure, Hodge, limit mixed      224 225 229 232 236 237
Structure, Hodge, mixed      210 213 215 218 219 221 224 226 237 242 245 246
Structure, Hodge, mixed on the Milnor bundle      239 241 244 250
Structure, Hodge, polarized      255 257
Structure, Hodge, pure      214
Study E.      199
Sub-analytic      187
Subgroup, arithmetic      257 526
Subgroup, Borel      460
Subgroup, isotropy      480
Subgroup, parabolic      256
Subset, Zariski closed      196
Subset, Zariski open      195
Subspace, holonomic      327
Subspace, horizontal      143 259
Summability      366
Suspension      79 138
Suzuki M.      412
Swallow tail      89
System of Fuchs class      294 315 320
System, distinguished of vanishing cycles      63 75 79 101
System, dual local      517
System, Euler— Poisson      435
System, Hamiltonian      159 164
System, Hamiltonian, completely integrable      136
System, Henon — Heiles      440
System, Jouanolou      397 410
System, local      141 208 224 270 496 516 527 535
System, Lotka — Volterra      159 166 191
System, Pfaff      183—185
System, reversible      191
System, root      82—85
System, root, irreducible      83
System, root, reduced      82 84 85
System, Yang — Mills      438
Szegoe G.      552
Szekers G.      353
Takens F.      164 341 426 555
Tanabe S.      537
Tarski A.      187
Teyssier L.      374 555
Theorem about action of monodromy on limit mixed I lodge structure      235
Theorem about action of monodromy on mixed Hodge structure on vanishing cohomology      215
Theorem about analt ic classification of abelian groups      421
Theorem about analytic classification of resonant diffeomorphisms      359
Theorem about analytic classification of resonant saddles      381
Theorem about analytic classification of solvable groups      424
Theorem about centralizer      421
Theorem about complement of discriminant      99
Theorem about existence and uniqueness of Picard — Vessiot extensions      445
Theorem about extraction of roots and embedding      358
Theorem about first integrals for Riccati equations      488
Theorem about formal classification of abelian groups      419
Theorem about formal classification of diffeomorphisms      348
Theorem about formal classification of solvable groups      423
Theorem about formal normal form for saddle-nodes      366
Theorem about generalized liouvillian extensions for n 2      457
Theorem about hypercohomology      205
Theorem about integrablity of hypergeometric equation      508
Theorem about limit mixed Hodge structure      230
Theorem about mixed Hodge structure on incomplete variety      221
Theorem about mixed Hodge structure on limit Milnor fiber      242
Theorem about mixed Hodge structure on semi-smooth variety      219
Theorem about monodromy for holomorphic function      1
Theorem about normality of Picard Vessiot extension      449
Theorem about primitive elementary extensions      460
Theorem about regularity of Gauss — Manin connection      146
Theorem about semi-stable reduction      108
Theorem about solution in quadratures      455
Theorem about subgroups of Galois group      450
Theorem about topological classification of diffeomorphisms      348
Theorem about variation monodromy group and integrability      437
Theorem of muteness of number of limit cycles      163
Theorem, A'Campo      115
Theorem, Abel — Ruffini      478
Theorem, Alexander duality      47
Theorem, analytic Hadamard — Perron      367
Theorem, Baum — Bott      409
Theorem, Bautin      189
Theorem, Bendixson — Seidenberg — Dumortier — van den Essen      342
Theorem, Bolibruch      307
Theorem, Borel — Ritt      154 365
Theorem, Briuno      381 382 385 386
Theorem, Chevalley      446
Theorem, Chow      415
Theorem, Cohen      431
Theorem, Darboux      395
Theorem, de Rham      50
Theorem, Dekkers      314
Theorem, Deligne      215
Theorem, Deligne — Fulton — Zariski      96
Theorem, division      20 21
Theorem, Dolbeault      198
Theorem, Dulac — Rapteyn      191
Theorem, Ecalle — Voronin      352
Theorem, Elizarov      376
Theorem, Factorization      28
Theorem, formal classification in nonresoant case      279
Theorem, formal normalization      280
Theorem, Frobenius      334
Theorem, fundamental of differential Galois theory      454
Theorem, fundamental of Galois theory      474
Theorem, Gabrielov      183 186 187
Theorem, Gelfand — Karpanov — Zelevinsky      530
Theorem, Givental      535
Theorem, Givental — Schechtman      535
Theorem, Griffiths transversality      258
Theorem, Grobman — Hartman      160
Theorem, Grothendieck — Birkhoff      299 302
Theorem, Hartogs      135
Theorem, Hilbert about zeroes      24
Theorem, Hilbert on basis      190
Theorem, Hironaka      103
Theorem, Hodge      199
Theorem, Hodge expansion      201
Theorem, Hudai — Verenov      413
Theorem, Hukuhara — Kimura — Matuda      see theorem about sectorial normalization for saddle-node
Theorem, Il'yashenko      416
Theorem, infinitesimal      261
Theorem, invariant cycle      238
Theorem, Jouanolou      398
Theorem, Koebe      386
Theorem, Kolchin about algebraic structure of Galois group      449
Theorem, Kostov — Bolibruch      314
Theorem, Lappo-Danilevskij      314
Theorem, Lefschetz, about hyperplane section      250
Theorem, Lefschetz, fixed point      55
Theorem, Lefschetz, strong      201
Theorem, Leray — Schauder — Tikhonov      377
Theorem, Lins — Neto      408
Theorem, Liouville      162
Theorem, Liouville — Arnold      435
Theorem, Liouville, about elementary functions      461 468
Theorem, Malgrange — Miwa      324
Theorem, Malgrange — Sibuya      287
Theorem, Martinet — Ramis      372
Theorem, Milnor      63
Theorem, monodromy      112 235 262
Theorem, Newlander-Nirenberg      337
Theorem, normalization      107
Theorem, Perron — Frobenius      439
Theorem, Petrov      170
Theorem, Petrov — Rhovanski      177
Theorem, Phragmen — Lindeloef      433
Theorem, Phragmen — Lindeloef, for functional cochains      433 465
Theorem, Picard      507
Theorem, Picard — Deligne — Mostow      523
Theorem, Picard — Lefschetz      71
Theorem, Plemelj      434
Theorem, Plemelj — Roehrl      297
Theorem, Poincare duality      43
Theorem, Poincare — Dulac      270
Theorem, Poincare — Dulac, for diffeomorphisms      347
Theorem, Poincare — Hopf      9
Theorem, Prelle — Singer about elementary first integrals      469
Theorem, preparation, Thom — Martinet      20
Theorem, preparation, Weierstrass      20 21 23
Theorem, Puiseux      28
Theorem, Ramis, about differential Galois group      464 465
Theorem, Ramis, about rigidity of non-solvable groups      433
Theorem, Remmert      186
Theorem, Riemann about multivalued functions      295
Theorem, Schlesinger, about Galois group      462 475
Theorem, Schlesinger, about isomonodromic deformation      316
Theorem, Schwarz about holomorphic mapping      262
Theorem, Schwarz about spherical triangle      497
Theorem, Sebastiani — Thom      140
Theorem, sectorial normalization, for diffeomorphisms      353
Theorem, sectorial normalization, for differential system      283
Theorem, sectorial normalization, for saddle-node      369
Theorem, Shcherbakov — Nakai      432
Theorem, Siegel      381
Theorem, Singer about liouvilian first integrals      469
Theorem, Steenbrink about quasi-homogeneous singularities      247
Theorem, Stokes      53
Theorem, Takens      426
Theorem, Torelli      261
Theorem, Torelli, for curves      255
Theorem, Torelli, for multidimensional hypereliptic integrals      528
Theorem, Tougeron      13 15
Theorem, Varchenko about basis      527
Theorem, Yoccoz      381 382 389 391
Theorem, Zariski van Kampen      93 94
Theorem, Ziglin about Euler-Poisson system      436
Theory, bifurcation      160
Theory, catastrophe      89
Theory, Galois      441
Theory, Galois, algebraic      473
Theory, Galois, differential      441
Theory, Galois, topological      471
Theory, homotopy      55
Theory, Khovanski      183
Theory, Morse      7
Theory, quantum field      324
Theory, Ziglin      435 512
Thick monodromy      112
Thorn R.      viii 20 90 140 411 429 554 555
Tikhonov A.N.      377
Tikhonov topology      480
Torelli R.      255 261 555
Torsion      36
Torsion element      36
Torsion of almost complex structure      see tensor Nijenhuis
Torus, algebraic      452 526
Torus, exponential      463
Tougeron J.-C.      viii 13 15 360
Touzet F.      539
Transform, Borel      360 363
Transform, Laplace      360 362
Transformation, elliptic      335
Transformation, gauge      145
Transformation, holonomy      see transformation
Transformation, monodromy      28 374
Transformation, monodromy hyperbolic      335
Transformation, parabolic      335
Transformation, Picard — Lefschetz      70 114 233
Trivialization      132 134 144
Trivialization, basic      132
Turrittin H.      vii 280
Ueno K.      323 546
V-manifold      see orbifold
Valuation      293
Valuation, Levelt      304 308
Value, atypical      126 177
Value, bifurcational      160
Value, critical      3 4 58 62 68 92
Varadarajan V.S.      291 538
Varchenko A.N.      viii—xi 13 15 168 177 183 195 251 252 491 538 555 556
Variation of cycle      66
Variety, abelian      255
Variety, algebraic      195
Variety, algebraic, closed      196
Variety, algebraic, quotient      107
Variety, algebraic, reduced      106
Variety, algebraic, smooth      196
Variety, Calabi — Yau      260
Variety, center      191
Variety, flag      256
Variety, Grassniann      256 258
Variety, Hermitian      198
Variety, normal      106
Variety, normal at point      100
Variety, quasi-projective      196
Variety, semi-smooth      215
Vassiliev V.A.      538
Vector, horizontal      143
Vector, primitive      201
Vector, vacuum      325
Verlinde E.      331
Verlinde H.      331
Verma D.N.      531 533
Vessiot E.      vii 442 556
Voisin C.      556
Volterra V.      159 166
Voronin S.M.      ix 333 352 379 412 418 542 556
Vries de G.      322
Waerden van der B.L.      556
Wang H.C.      56
Wasow W.      viii 283 556
Watson G.N.      556
Weber H.      268 541
Weber W.E.      299
Weierstrass K.T.W.      20 21 23 275
Weierstrass polynomial      21
Weight of semi-invariant      451
Wells R.O.      556
Weyl H.      82 83
Whitney H.      18 301
Whitney sum      301
Whittaker E.T.      556
Witten E.      331 556
Yakovenko S.Yu.      168 177 179 545 551 557
Yang C.N.      145 438 440 534
Yau S.-T.      260
Yoccoz J.-C.      ix 333 379 381 382 386 390 551 557
Yomdin Y.      543
Yoshida M.      546
Zamolodchikov A.      534 535
Zariski O.      94 96 557
Zariski topology      446
Zegeling A.      547
Zelevinsky A.V.      529 530 543 556
Zeta function of diffeomorphism      113
Zeta function of monodromy      113
Ziglin S.L.      x xi 435 436 512 557
Zondek H.      539 548 553 555 557
1 2 3 4 5
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