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Zoladek H. — Monodromy Group
Zoladek H. — Monodromy Group

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Название: Monodromy Group

Автор: 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.

The material is addressed to a wide audience, ranging from specialists in the theory of ordinary differential equations to algebraic geometers. The book contains a lot of results which are usually spread in many sources. Readers can quickly get introduced to modern and vital mathematical theories, such as singularity theory, analytic theory of ordinary differential equations, holomorphic foliations, Galois theory, and parts of algebraic geometry, without searching in vast literature.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 580

Добавлена в каталог: 22.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
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
1 2 3 4 5
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