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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
Number, Stokes 280 Number, unipotent 120 Number, variation, till 301 Number, Weil 250 Ohasi S. 509 545 Okamoto K. 322 Okonek G. 302 551 Oleinik O.A. 250 Onsager L. 328 Oort F. 551 Operator, annihulation 325 Order of holomorphic form 147 Orhifold 110. see V-manifold Orientation 39 Ortis-Bobadilla L. 417 554 Ossa de la X. 201 Oval 77 118 P-set see set sub-analytic Painleve P. vii 318 322 513 551 Pair of groups 481 Pair of groups, almost normal 481 Parallel transport 112 Parkes L. 261 540 Partition of unity 53 Partition, baricentric 43 Partition, simplicial 39 Paul E. 551 Pauli W. 327 Perez-Marco R. 333 391 551 Period 254 273 275 439 Periodic trajectory see solution periodic Perron O. 367 439 Petrov G.S., ix 128 168 170 173 175 551 Petrovski I.G. 250 418 547 551 Petrovski — Oleinik inequalities 250 Pfaff J.H. 183 185 393 Pham F. 26 115 136 251 360 536 551 Phase 151 Phase portrait 159 Phragmen E. 433 Picard E. vii 65 67 70 71 110 128 130 133 401 442 491 507 515 523 552 Plemelj J. vii 296 305 306 434 552 Pliicker J. 408 Pochhammer L. vii 484 494 515 552 Poincare domain 347 Poincare H. vii—ix 9 43 45 54 168 190 347 382 552 Point, conjugate (on geodesic) 49 Point, critical 3 4 15 57 62 68 Point, critical of differential equation, movable 321 Point, critical of differential equation, nonmovable 321 Point, fixed 55 161 Point, fixed, hyperbolic 161 Point, non-degenerate 3 4 58 Point, periodic 113 Point, ramification 2 472 Point, singular of analytic set 27 59 107 Point, singular of differential equation of Fuchs type 271 Point, singular of differential system 269 Point, singular of differential system, irregular 269 279 Point, singular of differential system, of Fuchs type 271 311 Point, singular of differential system, regular 146 269 270 Point, singular of holomorphic foliation 394 Point, singular of holomorphic foliation, dicritical 340 Point, singular of holomorphic foliation, elementary 339 Point, singular of holomorphic foliation, resonant 340 Point, singular of vector field 7 160 Point, singular of vector field, degenerate 8 9 Point, singular of vector field, hyperbolic 160 Poisson bracket 436 Poisson S. 435 436 Polya G. 552 Pontryagin L.S. 168 552 Potential Gromow — Witten 261 Potential Yukawa 260 Prelle M.J. 469 552 Presheaf 51 Primitive element 473 Primitive parametrization 28 Principal part of geometrical section 148 Principle, argument 171 Principle, Descartes 176 Principle, Rolle 175 Problem of center 193 Problem of small limit cycles 193 Problem of Thorn 411 Problem, center-focus 342 Problem, inverse in differential Galois theory 466 Problem, nonlinear Riemann — Hilbert 412 413 Problem, Riemann — Hilbert 296 297 299 305 307 314 324 328 Problem, VH-th Hilbert 236 Problem, XVI-th Hilbert 163 418 Problem, XVI-th Hilbert, weakened 168 Proper preimage see strict transform Pseudo-group 418 Pseudo-reflection 86 Puiseux V.A. 28 Pure braid group see group braid colored Put van der M. 465 552 Pyartli A.S. 382 432 545 552 Pyramid 91 Quadrature 455 Quasi-isomorphism 207 R-matrix 533 534 R-rank 526 Radical of ideal 24 106 Radical, unipotent 460 Raghunathan M. 552 Ramis J.-R. ix—xi 333 360 366 372 379 433 464 508 549 550 552 Rank of vector field at singularity 344 Ray of division 283 Rebelo J.C 415 549 Reed M. 553 Relation, anti-commutation 326 Relation, commutation 326 Relation, Gauss 495 Relation, Hodge — Riemann 202 254—256 Relation, Serre 533 Rellich F. 197 Remmert R. 186 544 Residue class 106 Residuum of Gauss — Manin connection 233 Residuum, Poincare 220 Resolution of hypersurface 102 239 Resolution of singularity of function 102 Resolution of singularity of holomorphic foliation 339 427 Resolution of singularity of holomorphic foliation, good 340 Resolvent 204 Resonant relation 276 278 Resonant relation for diffeomorphisms 347 Retraction 56 Rey J. 353 Rham de G. 49 50 Riccati J. 321 460 Riemann G.F.B. vii 1 202 254 255 295 296 412 471 472 553 Riemann P-equation see equation Riemann Riemann surface 1 4 67 117 119 179 471 472 474 480 Rigidity 434 Ring of analytic functions 106 Ring of discrete valuation 293 Ring of invariants 107 Ring, differential 442 Ring, integrally closed 106 Ring, local 13 106 Ringed topological space 106 Risch R.H. 468 553 Ritt J.F. 154 365 468 553 Roehrl H. vii 296 553 Rolle M. 175 185 Root 82 85 Root, negative 82 Root, positive 82 Root, simple 82 Rosales-Gonzalez E. 417 554 Rosenlicht M. 468 553 Rossi H. 299 544 Roussarie R. 553 Rousseau C 553 Ruffini P. 478 s-function 479 Sad P. 333 404 411 540 Saddle 179 340 Saddle, generalized 427 Saddle-node 340 Saddle-node, generalized 427 Saito M. 553 Salem E. 413 550 Satake I. 266 Sato M. vii 324 553 Sauvage L. 305 553 Scardua B.A. 488 553 Schauder J. 377 Schechtman V.V. 535 543 Scherk J. 251 553 Schlesinger L. vii 316 441 462 554 Schmid W. ix 195 224 225 235 553 Schneider H. 302 551 Schneider T. 236 554 Schwarz derivative 498 Schwarz H.A. vii x 262 428 467 501 509 516 554 Sebastiani M. 140 554 Section of bundle 51 Section, geometrical 144 146 Section, horizontal 143 144 147 Sector of fall 370 Sector of jump 370 Seidenberg A., ix 187 333 342 554 Seifert H. 72 165 Self-intersection see index of intersection Semi-continuity of spectrum conjecture 150 Semi-invariant 451 Semi-stable morphism 108 Semi-stable reduction 108 Separatrix 162 411 Sequence, central deriative 418 Sequence, Gysin 56 Sequence, long exact of homotopy groups 56 Sequence, long exact of pair 40 Sequence, spectral 203 Sequence, spectral, Leray 208 209 Sequence, spectral, of hypercohomology groups 206 Sequence, spectral, weight 217 221 Sequence, Wang 56 238 Series, Gevrey 365 Series, hypergeometric 493 Serre, J.-R 85 201 554 Set, constructive 446 Set, forbidden 480 Set, irreducible 27 see Set, real analytic 59 186 Set, real semi-analytic 186 Shaefke R. 540 Shafarevich I.R. 554 Shcherbakov A.A. x 333 412 417 418 432 542 554 Sheaf 51 Sheaf, coherent 51 Sheaf, cohomological 207 Sheaf, constant 51 210 Sheaf, direct image of 52 see Sheaf, flabby 53 204 Sheaf, inverse image of 52 Sheaf, Leray 141 208 209 Sheaf, of holomorphic functions 51 Sheaf, of holomorphic logarithmic forms 220 Sheaf, of holomorphic logarithmic relative forms 226 Sheaf, of ideals 301 Sheaf, of relations 51 Sheaf, of sections of bundle 51 Sheaf, of smooth forms 50 51 53 Sheaf, of smooth functions 51 Sheaf, of vector fields 51 Sheaf, Stokes 286 Shimomura S. 546 Sibirski K.S. 193 554 Sibuya Y. 281 287 554 Siegel C.L. 254 381 554 Siegel upper half-plane 254 265 Sigma-process 340 see Simart G. 67 552 Simon B. 553 simplex 39 Simplex with coefficients in local system 517 Singer M.F. x 469 552 554 Singularity of type 13 30 34 99 243 Singularity of type 14 33 34 Singularity of type 34 Singularity, Bogdanov — Takens 341 Singularity, cusp 104 109 see Singularity, fold 34 76 see Singularity, Lagrangian of type A3 48 Singularity, m-modal 33 Singularity, nilpotent of holomorphic foliation 426 Singularity, normal crossings 96 103 216 224 Singularity, of type 13 34 Singularity, parabolic 34 76 Singularity, Pham 115 136 536 Singularity, Picard-Fuchs 145 Singularity, simple 33 76 100 157 Singularity, unimodal 34 76 Singularity, Whitney 18 Skoda H. 252 539 Soares M.G. 548 554 Sobolev S.L. 197 Solution, periodic 160 167 Solution, periodic, hyperbolic 161 Solution, separating 184 185 Space of resurgent functions 361 Space, Chebyshev 170 Space, Chebyshev, with accuracy 170 Space, classifying of Hodge structures see space period matrix Space, Eilenberg — MacLane 56 99 Space, Fock 325 Space, Fock, Bose — Einstein 325 Space, Fock, Fermi — Dirac 325 Space, moduli 252 351 355 Space, moduli, of algebraic curves 255 Space, moduli, of analytic varieties 258 260 Space, moduli, of elliptic curves 253 Space, period matrix 254 256 257 Space, Sobolev 197 Space, weighted projective 247 Spanier E. 555 Spectrum of critical point 148 252 Spectrum of ring 107 Spencer D.C 259 547 Spherical triangle 498 Spindler H. 302 551 Stabilizer 476 480 Star of a vertex 43 53 Star operation 196 Star operation, Hodge 199 Steenbrink J.H.M. viii ix xi 195 219 224 225 232 235 247 249—252 553 555 Stein K. 221 Stereographical projection 503 Stirling J. 158 Stokes G.G. vii 53 555 Stokes phenomenon, linear 283 Strelcyn J.-M. 549 Strict transform 104 105 Strozyna E. xi 426 555 Structure, almost complex 336
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