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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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Hukuhara M. vii ix 280 369 376 509 545 Humphreys J.E. 545 Hurwitz A. 472 Hyperbolic measure 523 Hyperbolic metric 262 506 Hyperbolic motion 521 Hypercohomology 203 Ideal of denominators 448 Ideal, Bautin 190 Ideal, differential 442 Ideal, gradient 13 Ideal, maximal 13 106 Ideal, prime 446 Ideal, proper 446 Ideal, radical 106 Il'yashenko Yu.S. x xi 163 166 168 296 333 348 379 412 413 416 418 432 433 465 538 542 543 545 Ince E.L. 545 Index, Camacho — Sad, of branch 404 408 Index, Camacho — Sad, of curve 404 Index, complex of oscillation 148 Index, complex of singularity 148 Index, Maslov 47 48 153 Index, Morse, of critical point 10 Index, Morse, of geodesic 47 49 Index, Morse, of real quadratic form 10 Index, of fixed point of map 55 Index, of intersection 40 50 51 103 Index, of intersection, local 40 Index, of oscillation 157 158 Index, of singular point of vector field 7 15 24 27 29 343 Index, of singularity 157 Index, ramification 472 Index, ramification, (for differential system) 281 Infinitesimal period relations see condition transversality Integral domain 446 Integral, abelian 159 164 168 177 193 296 Integral, Chebyshev 486 Integral, Darboux — Hyperelliptic 486 Integral, Darboux — Schwarz — Christoffel 428 see Integral, Darboux — Schwarz — Christoffel, multiple 486 Integral, elliptic 117 118 128 170 267 273 Integral, elliptic, incomplete 273 502 Integral, first 395 467 Integral, Fresnel 152 Integral, generalized Abelian 194 Integral, higher order Melnikov 193 Integral, hypergeometric, multiple 527 528 530 536 Integral, Laplace 158 Integral, oscillating 150 151 154 157 Integral, Schwarz — Christoffel 416 428 501 Integral, Singer 483 485 488 Invariant of formal classification 348 Invariant, Gromow — Witten 255 Invariant, Katz 281 inversion 497 Ising E. 328 Ising model 328 Iwasaki K. 546 J-invariant 507 Jabotinsky E. 353 Jacobi K.G.J. 253 255 268 Jacobian of curve 253 Jaffe A. 543 Jeanquartier P. 546 Jet of germ 13 Jet, sufficient 15 Jimbo M. vii 323 324 532 546 553 Join of spaces 40 Jouanolou J.P. x 397 Kac V.G. 531 532 546 Kaehler E. 199 Kamke E. 467 487 546 Kampen van E.R, 94 Kaneko J. 546 Kaplansky I. 442 Kapteyn W. 191 Karpanov M.M. 529 530 543 Katz N. viii 279 292 541 546 Katz rank 293 Katz S. 540 Khibnik A.I. 166 Khizlmik V. 534 Khovanski A.G. vii ix 168 177 183 184 441 465 477 479 487 Killing W. 85 Kimura T. ix 353 369 376 508 545 546 Kirillov A.A. 547 Klein F. vii 491 547 Kobayashi S. 547 Kodaira K. 201 259 547 Koebe P. 386 Kolchin E. vii 449 547 Kontsevich M. 5 17 Kooij R.E. 547 Korteweg D. 322 Kostov V.P. 314 547 Koszul J.L. 228 Kovacic J.J. 490 Kowalewska case 436 Kowalewska S.V. 436 Kozlov V.V. 538 Krauskopf B. 166 547 Kuczma M. 353 17 Kuenneth H. 40 Kulikov V.S. 251 547 Kuranishi M. 260 Kurchanov P.V. 547 Lagrange case 435 Lagrange J.L. 435 438 Laguerre E. 268 Lamangian submanifold 17 Landis E. 418 547 Landman A. 112 209 548 Laplace P.S. 158 196 360 362 Laplacian 196 Lappo-Danilevskij, I. 314 548 Lattice 279 523 Lattice in module 293 Lattice, Brieskorn 279 Lattice, non-arithmetic 526 Laurieella G. 515 548 Lazzeri F. 101 Leaf 334 Leaf, algebraic 393 394 Leau L. 353 548 Lefschetz S. 55 65 67 70 71 110 126 201 250 278 548 Legendre A.M. 268 Lemma about long exact sequence 54 Lemma about prolongation of homotopy 56 Lemma about rational envelopes 177 Lemma, 198 Lemma, 218 Lemma, Cartan B. 221 298 299 Lemma, Hadamard 3 6 Lemma, holomorphic Poincare 127 204 Lemma, Khovanski — Rolle 185 Lemma, Morse 3 Lemma, Morse, with parameters 29 Lemma, Nakayama 22 Lemma, Poincare 54 Lemma, Rellich 197 Lemma, Sauvage 305 Lemma, Sobolev 197 Length of root 83 Leray J. viii 52 122 208 377 Leszczynski P. xi 194 548 Levelt A.H.M. vii 280 304 308 548 Levi-Civita T. 143 Levinson N. 540 Lie M.S. 85 Lindeloef E. 433 Linearization of XVI-th Hilbert problem see problem XVI-th Hilbert weakened Linking coefficient see number linking Lins-Neto A. x 333 405 406 408 413 485 538 548 Liousse I. 538 Liouville J. 47 162 435 468 548 Liverpool L.S.O. 353 Lobachevski N.I. 506 Lobachevski plane 506 Logarithm 455 Lojasiewicz S. 22 548 Loop, separatrix 162 Loop, simple 70 74 Loray F. xi 353 415 418 426 538 548 549 Lorenz H.A. 327 Lotka J. 159 166 Lukashevich N.A. 544 Lyapunov A.M. 190 549 Lyashko O.V. 538 Maciejewski A. xi 549 MacLane S. 56 Magid A.C 442 445 549 Mahoux G. xi 321 549 Malgrange B. viii 150 287 324 333 360 549 Malkin I.G. 193 Manifold, center 367 Manifold, Frobenius 330 331 Manifold, incomplete 219 Manifold, Kaehler 199 214 Manifold, orientable 39 Manifold, Stein 221 Manifold, strong 367 Manifold, symplectic 47 Manin Yu. I. 140 142 322 549 Map, Abel — Jacobi 253 255 Map, conformal 503 Map, etale see covering Map, Gysin 222 Map, Kodaira — Spencer 259 Map, period 195 224 252 253 258 259 263 521 528 Map, Pham 26 Map, Poincare see map return Map, proper 186 Map, quasi-conformal 338 Map, return 161 167 190 193 Map, Schwarz 496 521 Map, Schwarz — Christoffel 501 Map, Schwarz, generalized 521 Margulis G.A. 526 Martinet J. viii ix 20 333 360 366 372 549 Maslov V.P. 47 48 153 Maszczyk T. xi 6 Mathieu E.L. 268 Matrix, Cartan 82 Matrix, Cartan, generalized 532 Matrix, Coxeter 86 Matrix, Dirac 327 Matrix, fundamental 269 Matrix, monodromy 269 Matrix, Pauli 327 Matrix, period 132 254 Matrix, Stokes 286 Mattei J.F. 342 379 412 413 540 550 Matuda T. ix 369 376 545 Maxwell stratum 90 Mazzocco M. 513 514 541 Melnikov V.K. 168 550 Meromorphic operation 480 Method, homotopy 15 Method, Laplace 158 Meziani R. 426 Milinan P.D. 103 Mills R. 145 Milnor fibration see bundle Milnor Milnor J. viii 13 63 92 136 140 550 Mirror Symmetry 260 Miwa T. vii 323 553 Mjuller B. 415 550 Module over local ring 20 Module over ring of holomorphic functions 279 Module, Fuchsian 293 Module, Verma 531 533 Modulus of annulus 339 Modulus of formal classification 367 Modulus of quadrangle 339 Modulus of quasi-conformal map 338 Modulus, Ecalle — Voronin 353 Modulus, Malgrange — Sibuya 289 Modulus, Martinet — Ramis 366 Monk- algebraic equation 106 Monodromy pair 480 Monodromy pair, associated with forbidden set 480 Monodromy pair, closed 480 Moody R.V. 531 532 Morales-Ruiz J.J. xi 508 512 550 Mori A. 338 Morphism of mixed Hodge structures 213 Morse M. 3 7 10 29 47 49 Mostow G.D. x 491 515 516 523 526 541 550 Moulin-Ollagnier J. 549 Moussu R., x 342 379 412 418 426 428 429 434 540 550 Multiplicily of diagonal point of Newton diagram 158 Multiplicily of germ of function see number Milnor Multiplicily of singular point of vector field 15 25 Multiplier, characteristic 161 Multiplier, integrating 395 Muniford D.B. 108 255 260 541 550 Nakai I. x 432 Nakayama T. 22 Narasimhan E. 539 Neishtadt A.I. 166 538 551 Newell A. 323 542 Newlander A. 337 338 Newton I. 148 Newton polyhedron 148 Newton support 31 Nijenhuis A. 337 Nijenhuis tensor 337 Nilsson class 303 Nilsson N. 363 Nirenberg L. 337 338 547 551 Node 179 340 Nomizu K. 547 Nonlincarity 501 Norm mapping 327 Normal form of function 18 Normal form, Takens 427 Normal ordering mapping 327 Normal tower 181 Normalization 102 normalizer 263 476 Novikov D. 169 551 Novikov S.P. 541 Nowicki A. 549 Number, Betti 38 Number, cohomological 277 Number, creation 325 Number, field 325 Number, Hodge 214 246 247 256 Number, Laplace — Beltrami see laplacian Number, Lefschetz 55 201 Number, Leray coboundary 122 Number, linking 46 Number, Milnor 13 Number, monodromy 68 69 72 74 110 114 125—127 137 147 224 232 233 235 244 245 202 209 301 404 Number, of classical monodromy see transformation Picard — Lefschetz Number, of relative monodromy 69 Number, Poincare — Lyaptinov focus 190 Number, quasi-unipotenl 1 12 Number, resonant 437 Number, semi-simple 120
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