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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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Equation, Laguerre 268 Equation, Legendre 268 506 Equation, Mm In.mi 268 Equation, normal variation 436 439 512 Equation, Painleve 318 320—322 513 Equation, Pfaff 185 393 Equation, Picard — Fuchs 128 130 133 144—146 174 267 269 274 278 Equation, reducible 510 Equation, Riccati 321 Equation, Ricinann 492 Equation, Schlesinger 316 Equation, Schwarz 498 Equation, variation 136 Equation, wave 150 Equation, WDVV 331 Equation, Weber 268 Equation, Yang — Baxter 534 Equivalence of deformations 17 Equivalence of diffeomorphisms, formal 346 Equivalence of diffeomorphisms, holomorphic 346 Equivalence of diffeomorphisms, topological 346 Equivalence of differential systems formal 275 Equivalence of differential systems, holomorphic 275 Equivalence of differential systems, meromorphic 275 Equivalence of divisors 401 Equivalence of germs of functions, stable 30 Equivalence of groups, formal 418 Equivalence of groups, holomorphic 418 Equivalence, homotopical 38 Equivalence, left right 18 Equivalence, orbital, formal 366 Equivalence, orbital, holomorphic 366 Equivalence, orbital, topological 366 Equivalence, right 17 Equivalence, V-equivalence 18 Erdelyi A. 538 Erdoes P. 353 Essen van den A. 333 342 542 Euler case 135 Euler characteristic 9 38 Euler characteristic, intristic 105 Euler class 402 Euler L. 9 393 402 428 435 438 542 Expansion, asymptotic 154 Expansion, Gevrey 365 378 Expansion, Lefschetz 201 Expansion, Puiseux 28 EXPONENT 155 Exponent of quasi-homogeneous function 32 Exponent, Levelt 491 492 495 Extension by adjoining element 442 Extension, elementary 455 Extension, Galois 473 Extension, generalized liouvillian 455 Extension, liouvillian 155 Extension, normal of algebraic fields 473 Extension, Picard — Vessiot 442—445 448 450 453—455 457 Extension, radical 477 Extension, simple 473 Fabry E. 280 542 Fatou P. 353 Fermi E. 325 Fiber of bundle 51 Field of constants 442 Field of directions 335 Field of quotients 446 Field vector, Euler 393 Field vector, quasi-homogeneous Euler 428 Field, differential 442 Field, Yang — Mills 145 Filtration 205 Filtration by order of pole 252 Filtration by order of poles 220 Filtration, bete 215 Filtration, Hodge 213 217 222 225 230 235 529 Filtration, Hodge, asymptotic 249 251 252 Filtration, Hodge, standard 215 Filtration, quasi-homogeneous 32 Filtration, stupid see filtration bete Filtration, weight 213 217 225 230 Filtration, weight, asymptotic 251 Filtration, weight, monodromy 225 245 Flaschka H. 323 542 Fock B. 325 Focus 340 fold 18 Foliation 334 Foliation, holomorphic 179 333 334 Foliation, holomorphic, nonlinear Fuchsian 412 Foliation, Seifert 165 Fomenko A.T. 541 Form of type (p,q) 197 199 Form, Cartan — Killing 85 261 Form, closed 50 Form, connection 400 Form, exact 50 Form, Fubini — Study 199 Form, Gelfand — Leray 123 124 130 133 144 155 Form, harmonic 196 197 199 Form, holomorphic 119 122—125 144 198 203 302 Form, intersection 43 72 74—77 246 Form, Liouville 47 Form, polarization 202 203 255 Form, quadratic of singularity 75 Form, Seifert 72 Form, volume 196 Formula, adjunction 403 Formula, Baum — Bott 409 Formula, Campbell — Hausdorff 423 Formula, Cartan 334 Formula, Euler 494 Formula, Picard — Lefschetz 65 66 73 135 Formula, Picard — Lefschetz, twisted 535 536 Formula, Pluecker 408 Formula, Riemann — Hurwitz 472 Formula, Runneth 40 Formula, stationary phase 152 Formula, Stirling 158 Forster O. 542 Francoise algorithm 194 Francoise J.-P. 194 543 Fresnel A.J. 152 Frobenius F.G. 330 331 334 439 Fubini G. 199 Fuchs R. vii 128 130 133 271 294 321 543 Fuchsian weight of monodromy group 312 Fuchsian weight of system 311 Fulton W. 96 Function, algebraic 119 120 179 268 295 471 474 Function, almost normal 480 Function, Bessel 292 Function, Darboux 289 395 467 484 485 Function, Darboux — Schwarz — Christoffel 467 Function, elementary 455 461 468 Function, elliptic 439 Function, expressed by generalized quadratures see function generalized liouvillian Function, expressed by quadratures see function liouvillian Function, generalized Darboux 395 467 484 Function, generalized liouvillian 455 458 459 469 Function, hypergeometric 493 Function, hypergeometric, generalized 515 Function, irreducible 27 Function, liouvillian 455 Function, Lyapunov 190 191 Function, modular 506 Function, Morse 5 10 62 68 90 92 Function, primitively elementary 455 461 Function, probability 461 Function, quasi-homogeneous 32 246 Function, regular 446 Function, Schwarz, generalized see map Schwarz generalized Function, semi-quasi-homogeneous 33 Function, Weierstrass 275 Function, weighted homogeneous see function quasi-homogeneous Fundamental domain 506 Gabrielov A.M. 101 183 186 187 543 Galois E. 443 Gambier B. 321 Gamier R. vii 543 Garding G.W. 197 Garding inequality 197 Gauss F.C 140 142 267 493 543 Gavrilov L. 194 543 Gegenbauer L. 268 Gelfand I.M. x 123 491 529 543 556 Gelfand S.I. 538 Gelfond O.A. 236 543 Genus 253 Genus, algebraic 203 Genus, intristic 405 Genus, topological 203 Germ of function 13 Germ of function, infinitesimally stable 18 Germ of function, m-modal see singularity m-modal Germ of function, simple see singularity simple Germ of function, stable 18 Germ of function, unimodal see singularity unhnodal Gevrey M. 365 378 543 Ghys E. 386 Givental A.B. 261 535 543 Glimm J. 543 Glyutsuk A.A. 467 543 Godement P. 543 Golubev V.V. 491 544 Gordan P. 514 544 Goryunov V.V. 102 538 Grassmann H. 228 Grauert H. 544 Green P.S. 261 540 Griffiths P. viii ix 195 251 258 262 263 399 409 544 Grobman D.M. 160 Gromak V.I. xi 544 Gromov M. 331 Grothendieck A. viii 102 112 178 299 544 Group of analytic diffeomorphisms 418 419 421—424 427—432 Group of deck transformations 475 Group of multipliers 418 Group, abelian 418 419 Group, abelian, exceptional 419 Group, abelian, typical 419 Group, affine Weyl 83 Group, algebraic 450 Group, alternating 478 Group, braid 97—99 535 Group, braid, colored 98 521 533 534 Group, Clifford 326 327 Group, cohomology 35 36 Group, cohomology, Cech 52 400 Group, cohomology, Cech non-abelian 52 287 Group, cohomology, de Rham 19 Group, cohomology, Dolbeault 197 198 Group, cohomology, relative 39 Group, cohomology, with coefficients in local system 517 Group, cohomology, with compact support 46 517 Group, congruent 507 Group, Coxeter 82 87 Group, Coxeter, irreducible 86 Group, derivative 478 Group, dihedral 87 Group, extended mopnodromy 460 Group, finite 419 Group, formally linearizable 119 Group, Fuchsian 505 Group, fundamental 55 95 99 480 Group, Galois 473 Group, Galois, differential 443—445 449 450 454 455 457 460 462 464 512 Group, Galois, topological see group monodromy Group, generated by reflections 83 Group, generated by reflections, crystallographies 86 Group, holonomy 411 see Group, homology 35 Group, homology, Hochschild 533 Group, homology, locally finite see group homology with closed support Group, homology, reduced 39 Group, homology, relative 39 40 Group, homology, singular 35 Group, homology, with closed support 45 517 Group, homology, with coefficients in local system 517 Group, homotopy 56 Group, hypercohomology 205 207 217 220 227 Group, Klein 478 Group, Lorenz 327 Group, monodromy 68 92 257 270 411 429—431 474 483 531 535 Group, monodromy, associated with forbidden set 480 Group, monodromy, closed 480 Group, monodromy, extended 485 Group, monodromy, of hypergeometric integral with exponents 522 Group, monodromy, of pair 481 Group, Picard 401 Group, projective holonomy 411 Group, projective monodromy 497 502 507 509 516 521 Group, projective monodromy, reducible 510 Group, quantum 532 Group, quantum, Drinfeld — Jimbo 532 Group, reductive 452 Group, Siegel modular 254 Group, solvable 418 509 Group, solvable, exceptional 423 Group, solvable, typical 423 Group, spherical triangle 497 Group, spinor 327 Group, structural of bundle 401 Group, symmetric 98 100 Group, unipotent 452 Group, variation monodromy 436 Group, Weyl 82—84 86 87 100 Guckenheimer J. 90 Gunning R. 299 544 Gusein-Zade S.M. 13 15 538 Gysin W. 56 Hadamard J. 3 6 353 307 Hadamard regularization 520 Harris J. 399 409 544 Hartman P. 160 Hartogs F. 135 Hartshorne R. 544 Hausdorff F. 423 Hauser H. 103 544 Heading J.M.A. 292 544 Hecke E. 536 Heiles C 440 Henon M. 440 Hermite C 268 Hilbert D. vii 24 163 164 236 296 412 418 543 544 Hironaka H. viii 103 333 544 Hochschild G. 533 Hodge star see star operation Hodge W.V.D. 199 201 202 254 Homomorphism of cohomology groups 38 Homomorphism of diferential fields 442 Homomorphism of homology groups 38 Homomorphism, boundary 40 Homomorphism, connecting see homomorphism Homomorphism, connecting, boundary 234 Hopf E. 160 162 Hopf H. 9 532 Horizontal subbundle 259 Horozov E.I. 166 544 Huang K. 544 Hudai-Verenov M.O. x 413 545
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