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Vassiliev V.A. — Applied Picard-Lefschetz Theory
Vassiliev V.A. — Applied Picard-Lefschetz Theory

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Название: Applied Picard-Lefschetz Theory

Автор: Vassiliev V.A.

Аннотация:

Many classical partial differential equations in mathematical physics and other applied sciences have integral representations, i.e., are defined by integrals depending on parameters. This volume focuses on various versions of the Picard-Lefshetz theory and results that describe ramifications of four kinds of integral functions: volume functions, Newton-Coulomb potentials, fundamental solutions of hyperbolic partial differential equations, and multidimensional (Gelfand-Aomoto) hypergeometric functions. No information is provided on the author's affiliation, though 17 of his books on topology and related topics are listed among the 189 references.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 324

Добавлена в каталог: 22.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Adapted coordinates      98 150
Adjoint strata      76
Admissible chain      89
Algebraic body      111
Algebraic integrability      111
Arnold class      261
Arnold class, localized      270
Arnold class, projective      261
Arnold class, reduced      266 271
Arnold orientation      257
Base of deformation      45
Basic stratum      299
Bifurcation diagram of functions      63
Big monodromy group      268
Bistable equivalence      172
body      111
Body, algebraic      111
Body, non-singular      111
CAP      120
Cauchy problem      142
Caustic      63
Chain subanalytic      89
Chain subanalytic, admissible      89
Characterizing function      193
Charge, standard      255
Clemens structure      232
Codimension of a complete intersection      71
Cohomological bundle      29
Cohomology group of a local system      216
Complete intersection      71
Completely infinite reflection group      284
Completely real singularity      51
Complex link      82
Conditional integral      291
Corank of a singularities      57
Cuspidal edge, generic      126
Davydova — Borovikov condition      149 150
Deformation      45
Deformation of a complete intersection      72
Deformation, equivalent      47
Deformation, induced      47
Deformation, miniversal      48
Deformation, versal      47
Degenerate point      115
Diffusion of waves      144 145
Direct image of a local system      215
Discriminant      46
Discriminant of a complete intersection      73
Discriminant, real      65
Distinguished basis      42
Distinguished system of paths      40
Distinguished system of paths, perfect      278
Dual local system      218
Dual projective space      116
Dual set      79
Dynkin diagram      45
Element representable by a cap      120
Element representable by a vanishing cycle      120
Elliptic polynomial      258
Elliptic singularities      60
Equivalent deformations      47
First type cycle      279
First type point      279
Formal lacuna      166
Formal lacuna, even, odd      166
Fundamental solution      142
Fundamental solution, principal      143
Gauss — Manin connection      29
Generating family      122
Generating family, projective      148
Generating function      122
Generating function, projective      146
Generic cuspidal edge      116
Generic hyperplane      82
Gradient ideal      47
Graph of separatrices      51
Harm      96
Herglotz — Petrovskii — Leray integrals      151
Holomorphic lacuna      145
Holomorphic sharpness      145
Homological bundle      29
Homological covering      291
Homology group of a local system      216
Homology group with coefficients in the local system      216
Hyperbolic operator      142
Hyperbolic polynomial      140 256
Hyperbolic potential      258
Hyperbolic singularities      60
Hyperbolicity domain      141 257
Hyperplane arrangement      298
Hyperplane arrangement, basic      299
Hyperplane arrangement, essential      298
Hypersurface      35
Hypersurface, projectively dual      116
Imaginary cone      299
Induced deformations      47
Infertile segment of the queue      213
Integration cycle      291
Integration cycle, tame      291
Intersection matrix      44
Isolated singularity      37
Isolated singularity of a complete intersection      71
Lacuna      144
Lacuna, $C^{\infty}$-      145
Lacuna, holomorphic      145
Lacuna, local      137 145
Lacuna, strong      145
Laplace operator, standard solution of      255
Le number      83
Lefschetz thimble      50
Leray class      153
Leray coboundary operator      35
Leray cycle      153
Local algebra      48
Local lacuna      137 145
Local lacuna, projectivized      149
Local Petrovskii class      157
Local Petrovskii condition      156
Local system      215
Local system, dual      218
Localized homology group      157
Locally finite chain      216
Maxwell set      63 196
Milnor fibration      33
Milnor number      38
Milnor number of a complete intersection      71
Miniversal deformation      48
Mirage      306
Modality      58
Monodromy group      29
Monodromy representation      29
Morse function      38
Morse lemma      38
Morse singularity      38
Morsification      39
Morsification, strict      39
Morsification, virtual      209
Natural orientation      255
Negative index      173
Newton — Coulomb potential      255
Non-parabolic point of a stratum      80
Non-singular body      111
Obstructing germ of a curve      127
Obstructing stratum      127
Open stratum      298
Order complex      301
Orientation sheaf      215
Parabolic point      115
Parabolic singularities      60
Parts of a partition      79
Perversity      91
Petrovskii class, even      165
Petrovskii class, local      157
Petrovskii class, odd      165
Petrovskii condition      154
Petrovskii condition, local      156
Petrovskii cycle      153
Petrovskii local cycle, even      165
Petrovskii minus-condition      193
Petrovskii plus-condition      193
Picard — Lefschetz formula      33
Point of finite type      156
Potential      252
Potential function      255
Primary stratification      76
Principal fundamental solution      143
Projective duality      115
Projective generating family      148
Projective generating function      146
Proper cone      142
Proper modality      61
Purse      206
Pyramid      195
Quasihomogeneous function      59
Real discriminant      65
Real function      51
Regular adjacency of strata      76 77
Resolution of singularities      225
Resonance      292
Riemannian covering      217
Sabirization      51
Second type cycle      279
Second type point      279
Semialgebraic subset      78
Semianalytic subset      78
Separatrices      51
Separatrices, lower and upper      51
Separatrix diagram      51
Sharpness, $C^{\infty}$-      145
Sharpness, holomorphic      145
Simple loop      40
Simple singularities      57
Simple tangency      80 266
Simplicial resolution      302
Singularity      37
Singularity, completely real      51
Singularity, elliptic      60
Singularity, hyperbolic      60
Singularity, isolated      37
Singularity, isolated, of a complete intersection      71
Singularity, Morse      38
Singularity, Morse, stratified      92
Singularity, parabolic      60
Singularity, simple      57
Singularity, unimodal      60
Small monodromy group      268
Space of momenta      137 144
Stabilization      44
Stable front      148
Stable singularity $A_{3}$      148
Standard charge      255
Standard charge with density      256
Stratified Morse function      92
Stratified Morse singularity      92
Stratified submersion      78
Stratum      76
Strictly hyperbolic polynomial      140 256
Strictly Morse function      38
Strong lacuna      145
Subanalytic chain      89
Subanalytic subset      78
Swallowtail      46
Tarski — Seidenberg lemma      78
Thom Isomorphism      217
Thom isotopy lemma      78
Transversality      77
Transversality to a stratified set      77 80
Trivial extension      224
Trivial point      117
Tube operator      35
Two-index polynomial      200
Tyurina number      73
Unimodal singularities      60
Vanishing cell      35
Vanishing cycle      42
Vanishing sphere      33 41
Versal deformation      47
Vertex of an arrangement      299
Vieta map      62
Virtual Modification      209
Wave front      137 145
Wave front, stable      148
Whitney conditions      76 77
Whitney stratification      77
Whitney umbrella      88
Zone      252
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