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Golubitsky M., Guillemin V. — Stable Mappings and Their Singularities
Golubitsky M., Guillemin V. — Stable Mappings and Their Singularities

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Название: Stable Mappings and Their Singularities

Авторы: Golubitsky M., Guillemin V.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1974

Количество страниц: 209

Добавлена в каталог: 01.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\Gamma$ -structure      3
$\Gamma$-atlas      3
1-form      21
1-generic      144
2-generic      155
Baire space      44
Boardman map      157
Borel Extension Lemma      98
C* topology      42
Canonical bundle      21
Chart      3 74
Condition $\mathcal{O}$      116
Condition NC      157
Contact class      173
Contact equivalence germs      1 72
Contact equivalence k-jet submanifold germs      173
Contact equivalence k-jets      173
Coordinate neighborhood      5
Corank      33 60
Cotangent bundle      20
Covering      15
Critical point      33 115
Critical point, critical value      34
Critical point, non-degenerate      63
Cross cap      179 181
Curve      12
Cusp      146
Cusp simple      146 147
Deformation      118 120
Diffeomorphism      7
Differentiable      1 6
Differentiable class $C^k$      1 6
Embedding      7
Equivalent mappings      72
EXP      195
Family of vector spaces      18
Fiber bundle      41
Finite mapping      167
Fold locus      87
Fold point      87 146
Frechet space      74
General position      83 85
Generalized Malgrange Preparation Theorem      106
Generic property      141
Germs function      103
Germs mapping      111
Germs submanifold      170
Grassman manifold      4
hessian      64 132
Homogeneous space      198
Homotopic stability      119
Immersed submanifold      10
Immersion      6
Implicit function theorem      7
Index, bilinear form      65
Index, non-degenerate critical point      65
Infinitesimal generator      27
Infinitesimal stability germs      111
Infinitesimal stability mappings      73
Infinitesimal stability, local      111
Intrinsic derivative      64 150 151
Inverse function theorem      2
Isotropy subgroup      198
Jacobian      2 13
Jet bundle      37
Jet bundle of sections      112
Jets mappings      37
Jets submanifolds      172
k-deformation      120
kth order contact      37
Lie group      194
Lie group action      198
Lie group subgroup      196 207 208
Local coordinates      5
Local homeomorphism      2
Local infinitesimal stability      111
Local ring      103
Local ring of contact      170
Local ring of germs      173
Local ring of k-jets      173
Local ring of mappings      165
Local transverse stability      134
Manifold      3
Manifold class $C^\infty$      3
Manifold differentiable      3
Manifold smooth      3
Manifold, Banach      74
Manifold, Frechet      74
Manifold, orientable      3
Manifold, real analytic      3
Manifold, topological      3
Mather Division Theorem      95
Measure zero      30
Metric      21
Metric, Riemannian      21
Module      104
Module, finitely generated      104
Morin singularity      174
Morse function      63
Multijet bundle      57
Multijet transversality theorem      57
Multiplicity      168 169
Nakayama's lemma      104
Nirenberg Extension Lemma      98
Non-degenerate fixed point      59
Normal bundle      71
Normal crossings      82 157
Normal space      71
One parameter group      27
Orbit      72 198
Paracompact      15
Partition of unity      16
Product family      18
Proper mapping      11 25
Pseudogroup      2
Pull-back function      1
Pun-back bundle      73
Rank      6
refinement      15
Refinement, locally finite      15
Regular point      34
Regular value      34
Residual      44
s-fold k-jet bundle      57
Sard's theorem      34
Section      18 21
Singularity      143
Singularity contact class      173
Singularity critical point      33
Singularity cross cap      179 181
Singularity cusp      146
Singularity fold      87 88 146
Singularity multiplicity      168 169
Singularity simple cusp      146 147
Singularity swallow's tail      176 177
Singularity, elliptic umbilic      183 187
Singularity, hyperbolic umbilic      183 188
Singularity, Morin      174
Singularity, Morse      63
Singularity, non-degenerate      63
Singularity, parabolic umbilic      183 190
Singularity, type $S_r$      143
Singularity, type $S_{r,s}$      152
Singularity, umbilic      182
Smooth function      1 6
Smooth functor      19
Smooth manifold      3
Source      37
Stability      72
Stability mappings      72
Stability transverse      139
Stability under deformations      119
Stability under k-deformations      120
Stability, homotopic      119
Stability, infinitesimal      73
Stability, local infinitesimal      111
Stability, local transverse      134
Subbundle      26
Subbundle complementary      27
Submanifold      9
Submanifold, immersed      10
Submersion      6
Submersion with folds      87 88
Support functions      16
Support vector fields      28
Symmetric function      108 2
Tangent      12 75
Tangent bundle      14
Tangent space      12
TARGET      37
Thorn Transversality Theorem      54
Thorn — Boardman stratification      159
Transversality      50 54
Transverse stability      139
Trivial deformation      118 120
Trivial deformation family of vector spaces      18
Trivial deformation vector bundle      18
Trivial deformation, k-deformation      120 124
Tubular neighborhood      69
Tubular neighborhood theorem      69
Umbilic      182
Umbilic, elliptic      183 187
Umbilic, hyperbolic      183 188
Umbilic, parabolic      183 190
Vector bundle      18
Vector bundle base mapping      26
Vector bundle canonical bundle      21
Vector bundle cotangent bundle      20
Vector bundle homomorphism      18 26
Vector bundle isomorphism      18
Vector bundle tubular neighborhood      69
Vector bundle, jet bundle      41
Vector bundle, normal bundle      71
Vector bundle, pull-back bundle      73
Vector bundle, tangent bundle      12 75
Vector bundle, trivial bundle      18
Vector field      21
Vector field along f      73
Vector field left invariant      195
Vector field, compactly supported      28
Weierstrass division theorem      91
Weierstrass preparation theorem      91
Whitney $C^k$ Topology      42
Whitney $C^\infty$ Topology      42
Whitney embedding theorem      62
Whitney immersion theorem      61
Whitney sum      20
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