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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.
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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
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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
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