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Zoladek H. — Monodromy Group
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Название: Monodromy GroupАвтор: 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.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2006Количество страниц: 580Добавлена в каталог: 22.05.2008Операции: Положить на полку |
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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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