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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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A'Campo N. viii 114 537 Abel N.H. 253 255 353 478 Absolute 505 506 524 Adjoining of exponent of integral 444 Adjoining of integral 444 Ahlfors L.V. 338 537 Airy J.R. 268 Alexander J.W. 47 Alexandrov A.G. 537 Alexeev V.B. 537 Algebra, Clifford 326 Algebra, Grassmann 228 Algebra, group 532 Algebra, Hecke 536 Algebra, Hopf 532 Algebra, Kac — Moody 531 532 Algebra, Lie 85 Algebra, Lie, semi-simple 85 Algebra, Lie, solvable 85 Algebra, local 13 15 24 25 Algebra, Probenius 330 Algebra, universal 532 Alien derivation 364 Analytic element 1 Andronov A.A. 160 162 Anosov D.V. 302 537 Antipode 532 Aomoto K. 537 Arnold V.I. viii ix 13 15 100 150 168 247 250 382 435 477 537 538 Artin E. 98 538 Babbitt D.G. 291 292 538 Baily W.L. 262 263 538 Baker J.N. 353 Base of bundle 51 Base of deformation 17 Basis of root system 82 Basket 92 Bateman G. 538 Baum P.F. 409 538 Bautin N.N. 189 538 Baxter R. 534 Belliart M. 538 Beltrami differential 337 Beltrami E. 196 337 Bendixson I. 333 342 538 Berezovskaya F.S. 166 538 Bernoulli J. 428 468 Bernstein I.N. 538 Bers L. 338 Berthier M. 485 538 Bertrand D. 539 Bessel F.W. 268 Betti E. 38 Bieberbach conjecture 386 Bieberbach L. 386 Bifurcation, Andronov — Hopf 160 Bifurcation, Andronov — Hopf for diffeomorphisms 162 Bifurcation, Bogdanov — Takens 164 Bifurcation, period doubling see bBifurcation pitchfork Bifurcation, pitchfork 162 Bifurcation, saddle node for diffeomorphisms 162 Bifurcation, saddle-node 160 Birkhoff G.D. 288 299 353 539 Blowing-up 103 340 Blowing-up along subvariety 104 Blowing-up, polar 341 Bobiehski M. xi 194 539 Bogdanov R.I. 164 341 539 Bojarski B. 338 Bolibruch A.A. vii 297 302 307 314 537 Borel A. 112 262 263 538 Borodzik M. xi Bose S. 325 Bott R.H. 409 538 Boundary of chain 35 Boundary of singular cell 35 37 Bouquet, J.C 367 539 Bourbaki N. 539 Braaksina B.L.J. 285 Braid 97 Braid, non-knotted 97 Branges de L. 386 Briancon J. 252 539 Brieskorn E. 112 236 539 Briestone E. 103 539 Briot C.A. 367 539 Briuno A.D. ix 333 381 382 385 539 Browkin J. 540 Bundle, canonical 260 302 403 Bundle, fibre 51 Bundle, holomorphic 301 Bundle, line 51 301 Bundle, Milnor 60 62 72 92 136 140 239 Bundle, Milnor, cohomological 141 142 144 146 208 239 244 251 Bundle, Milnor, homological 140 Bundle, normal 402 Bundle, vector 51 399 Calabi E. 260 Camacho C. 333 404 411 540 Campbell J.E. 423 Canalis-Durand M. 540 Candelas P. 261 Cano P. 540 Canonical level 281 Cartan E. 82 85 143 261 334 532 Cartan H. 221 298 Cartan subalgebra 85 Caustic 48 89—91 151 153 Cech E. 52 Cell singular 35 37 Center 161 189 Center of foliation 416 Center, codimension four 192 centralizer 263 420 Cerveau D. x 418 426 434 485 538 540 Chain 35 Character of group 451 Chavarriga J. 540 Chebyshev P.L. 170 Chern class 399—401 Chern S.S. 400 401 Chevalley C. 126 450 Chevalley decomposition 126 Chmutov S.B. 556 Chow W.L. 415 Christofer C 469 Christoffel E.B. 416 428 467 Clemens C.H. viii 111 540 Clifford N.K. 326 Coboundary 36 Coboundary of Cech cochain 52 Cochain 36 Cochain, Cech 52 Cochain, functional 356 433 465 Cochain, normalizing 353 Cocycle 36 Cocycle, Cech 53 Cocycle, Stokes 289 Coddington E.A. 540 Codimension of saddle-node 367 Coefficient of embedding of Newton polyhedra 149 Cohen S. 431 540 Commensurability 526 Commutator of group 418 Compactification, algebraic 105 Compactification, Baily — Borel 262 263 Compactification, Satake see compactification Baily Borel Compactification, semi-stable 524 Compactification, stable 524 Complete class of pairs of groups 481 Complete class of pairs of groups, minimal 481 Complete integrability 435 Complete intersection 101 Complex reflection 521 Complex, acyclic see complex exact Complex, chain 36 Complex, chain, completed 39 Complex, cochain 36 Complex, de Rham of ring 251 Complex, Dolbeault 198 Complex, double 204 Complex, dual 43 Complex, exact 36 Complex, Hochschild 533 Complex, holomorphic de Rham 204 Complex, Koszul 228 Complexification of real manifold 336 Comultiplication 532 Condition, Briuno 382 386 388 390 422 Condition, Fuchs 492 Condition, integrality INT 522 Condition, transversality 258 Connection 142 317 Connection in module 293 Connection, compatible with complex structure 400 Connection, compatible with metric 400 Connection, flat 143 Connection, Gauss — Manin 140 142—144 147 208 224 232 233 258 267 274 278 517 527 Connection, Levi-Civita 143 Connection, regular 293 Connection, separatrix 162 Continued fraction 382 384 Contraction, Clemens 110 111 209 Contraction, thick Clemens 112 Convolution 362 Coorientation 47 Corank of singularity 30 Counit 532 Covering 51 Covering, Galois 475 Covering, ramified 2 471 472 Cox D.A. 540 Coxeter graph 86 Coxeter H.S.M. 82 86 540 Cremer H. 382 385 540 Cristoffel E.B. 501 Cup-product 50 Curvature 143 317 Curve, algebraic 203 253 Curve, elliptic 117 128 169 202 252 439 Curve, hyperelliptic 130 253 Curve, invariant 394 Curve, phase 159 Cusp 18 88—91 Cusp point 524 Cusp, generalized 427 CW-complex 35 CYCLE 35 Cycle with closed support 45 Cycle, fundamental 39 Cycle, limit 161 163 164 167 Cycle, limit, of foliation 416 Cycle, locally finite 45 Cycle, Pochhammer 484 494 518 Cycle, vanishing 6 62 63 67 125 Darboux G. 395 467 540 Davenport J.H. 540 Dedekind R.J.W. 299 541 Deformation 17 Deformation retract 50 Deformation, induced 17 Deformation, infinitesimal of variety 259 Deformation, infinitesimally versal 19 Deformation, isomonodromic 315 Deformation, mini-versal 17 88 92 100 135 Deformation, restricted mini-versal 89 90 Deformation, versal 17 Degeneration of algebraic varieties 105 114 239 Degeneration of algebraic varieties, semi-stable 229 238 Degree of covering 472 Degree of foliation 393 Degree of line bundle 402 Degree of map 8 39 Degree of quasi-homogeneous function 32 Dekkers W. 314 541 Deligne P. viii—x 90 215 219 225 450 541 Derivation 442 Descartes R. 170 Diagonal of quasi-homogeneous function 32 Diagram, bifurcational, of function 90 Diagram, bifurcational, of zeroes 88 92 100 Diagram, Dynkin, of root system 83 85 88 Diagram, Dynkin, of singularity 75 76 79—81 Diagram, Newton 31 148 157 Diffeomorphism, holonomy 415 Diffeomorphism, monodromy 69 see Diffeomorphism, tangent to identity 348 Dijkgraaf R. 331 Dilation 500 Dirac P.A.M. 325 327 Discriminant set 99 Distance of Newton diagram 149 157 Distance of polyhedrons 149 Distribution in tangent bundle 143 334 Distribution in tangent bundle, integrable 334 Distribution in tangent bundle, involutive 334 Divergence (of vector field) 162 Divisor 301 399 401 Divisor of zero 107 446 Divisor, dicritical 341 Divisor, exceptional 104 Divisor, principal 401 Dolbeault P. 198 Douady A. 386 Drinfcid V.C 532 Duality, Kodaira — Serre 201 Duality, Poincare 45 47 517 Dubrovin B.A. vii 330 331 513 514 Dulac criterion 161 Dulac H. 161 163 191 347 541 Dumortier F. 333 342 542 Dyed braid group see group braid colored Dynkin E.B. 75 83 Ecalle composition 363 Ecalle J. ix 163 333 352 360 364 365 Effective action 453 Ehresmann C. 542 Eilenberg S. 56 Einstein A. 325 Element algebraic 455 Elementary catastrophes 90 Elizarov P.M. 333 373 376 379 412 Equation of Fuchs class 294 Equation, Airy 268 458 Equation, Beltrami 337 Equation, Bernoulli 428 468 Equation, Bessel 268 291 459 466 Equation, bridge 365 Equation, Cartan structure 143 Equation, defining 273 491 Equation, Euler 271 Equation, Euler — Lagrange 138 Equation, Gauss 267 493 508 512 Equation, Gauss hypergeometric 491 Equation, Gegenbauer 208 Equation, Hermite 268 Equation, hypergeometric confluent 268 Equation, Jacobi 268 Equation, Khizhnik — Zamolodchikov 534 Equation, Korteveg de Vries 322
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