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Goryunov V.I., Lyashko O.V. — Dynamical Systems VI: Singularity Theory I, Vol. 6
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Название: Dynamical Systems VI: Singularity Theory I, Vol. 6Авторы: Goryunov V.I., Lyashko O.V. Аннотация: The theory of singularities is an important part of various branches of mathematics: algebraic geometry, differential topology, geometric optics, etc. Here the focus is on the singularities of smooth maps and applications to dynamical systems - in particular, bifurcations. This includes the study of bifurcations of intersections of stable and unstable cycles. Along with the formal algebraic and analytic aspects of the theory, the authors consider global topological problems related to invariants. The authors have in mind a student reader, mathematician, or physicist, who wishes to learn the modern techniques of local mathematical analysis as an instrument for applied studies or a specialist in one of the applied areas who is looking for the necessary mathematical tools.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1993Количество страниц: 245Добавлена в каталог: 08.04.2008Операции: Положить на полку |
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151 18 22 Adjacency of singularities 30 Afra 222 Alekseev, A.V. 206 221 Algebra, DA 170 Algebra, DA-, local — of a map 38 157 Algebra, DA-, local — of a singularity 113 Algebra, DA-, of quasijets 37 Arnol’d, V.I. 8 9 12 14 16—18 20 24 30 33 38—44 46 47 66 70 71 82 83 101 112 114 117 118 125—127 129—132 140 143 146 151 161 163 165 168—170 174 183 192 199 203 207 210 211 215—218 221-223 Artin — Brieskorn braid group 124 Atiyah, M.F. 119 223 Audin, M. 200 223 A’Campo, N. 70 72 87 103 221 Bakhtin, V.I. 152 153 183 223 Banchoff, T. 202 223 Baryshnikov, Yu.M. 218 Basis of vanishing cycles, distinguished 60 Basis of vanishing cycles, weakly distinguished 60 Basset, A.B. 117 223 Beauville, A. 117 223 Belitski 174 179 223 Benson, M. 38 223 Bernshtein, D.N. 162 163 223 Bierstone, E. 168 171 223 Bifurcation set, function 21 Bifurcation set, level 19 Bimodal function 18 Bimodal function singularity 18 Boardman symbol of an ideal 154 Boardman, J.M. 153 154 223 Bordism 187 Borel, A. 186 223 Bourbaki, N. 39 40 119 127 223 Br 221 224 Braid group 65 Braid group, Artin — Brieskorn 124 Brieskorn, E. 27 31 60 65 71 86 87 91 92 94 95 97 124 143 223 224 Bruce, J.W. 117 136 174—176 221 224 Bryzgalova, L.N. 181 224 Bundle, cobordant to zero 195 Bundle, cohomology 89 Bundle, flag 189 Bundle, Grassmann 188 Bundle, homology 90 Bundle, normal 190 201 Bundle, vanishing cohomology 90 Bundle, vanishing homology 90 Bundle, vector 139 Byaly 211 224 Cerf, J. 216 224 Chamber 120 Characteristic class 191 Characteristic number 205 Chern class 187 Chern, S.S. 106 224 Chess, D.S. 191 224 Chislenko, Yu.S. 133 224 Chmutov, S.V. 8 87 88 115 224 225 236 Class, characteristic 191 Class, Chern 187 Class, fundamental homology 186 Class, of multisingularities 204 Class, of singularities 22 Class, Pontryagin 192 Class, stable cohomology — of complements of discriminants 145 Class, Stiefel — Whitney 139 Class, total Stiefel — Whitney 188 Class, universal Stiefel — Whitney 139 Classical-monodromy operator 53 Classification 193 Classification, stable 199 Codimension of a germ 166 Codimension of a germ, extended 166 Coexistence of singularities 198 Cohen, F.R. 140 225 Cohen, R.L. 213 225 Cohomology bundle 89 Cohomology bundle, vanishing 90 Cohomology ring, local 144 Complex of singularities, multisingularities 203 Complex of singularities, universal 193 Coorientation 192 Corank of a critical point 11 Coxeter graph 120 Coxeter group 119 Coxeter number 122 Coxeter representation of a group of permutations (reduced) 141 Coxeter transformation 122 Critical extension 154 Critical point 10 Critical point of a map 148 Critical point, isolated (of finite multiplicity) 13 Critical point, Morse (nondegenerate) 11 Critical points, equivalence 11 Critical value 10 Cusp 149 DA-algebra 170 Damon, J. 170—174 182—18 5 225 Danilov, V.I. 112 163 225 Deformation 15 167 Deformation, induced 15 167 Deformation, infmitesimally versal 17 168 Deformation, miniversal 15 Deformation, of finite codimension in positive weights 185 Deformation, topologically trivial 183 Deformation, truncated versal 20 Deformation, versal 15 17 167 Deformation, versal in weights 184 Deformations, equivalence 15 Degree of a monomial 37 Degree of a monomial, Newton 45 Deligne, P. 97 105 124 130 143 225 226 Demazure, M. 76 132 226 Diffeomorphism, formal 41 Diffeomorphism, of order 41 Diffeomorphism, quasihomogeneous 41 Differential condition (relation) 214 Differential condition (relation), prolongable 215 Dimca, A. 161 226 Dimensions, nice 160 Dimensions, semi-nice 160 Direct sum of singularities 75 Discriminant 19 Dolgachev, I.V. 28 226 Double of a manifold with boundary 209 du Plessis, A. 161 174—176 178 179 215 224 227 232 233 Du Val, P. 27 235 Dufour, J. — P. 169 226 Durfee, A.H. 114 226 Dyer, E. 140 226 Dynkin diagram 64 128 Ebeling, W. 84 86 87 226 Eilenberg — Mac Lane space 66 Eisenbud, D. 164 226 Eliashberg, Ya.M. 214 226 228 Elkik, r. 115 226 Elliptic singularity 82 Equivalence of critical points 11 Equivalence, 22 Equivalence, contact ( 156 Equivalence, contact functions 22 Equivalence, contact sections 100 Equivalence, left ( 149 Equivalence, right 149 Equivalence, right-left 148 Equivalence, stable 12 63 Equivalence, weak homotopy 213 Feit, S. 214 226 Flag bundle 189 Fold (pleat) 149 Foliation 196 Foliations, related 196 Fuks, B.A. 91 226 Fuks, D.B. 125 138—140 196 226 227 Fukuda, M. 182 227 Fukuda, T. 182 227 Function bifurcation set 21 Function, bimodal 18 Function, quasihomogeneous 36 Function, real 72 Function, semi-quasihomogeneous 37 Function, simple 18 Function, unimodal 18 Functions, equivalence 22 Fundamental homology class 186 Gabrielov, A.M. 18 20 21 70 75—77 79 83 115 227 Gaffney, T. 162 167 174 183 184 191 224 225 227 Genotype 157 Genus of a map 142 Geometric genus 115 Geometric genus, nice 173 Geometric genus, principal part 108 Geometric section 92 Geometric subgroup 172 Germ of finite multiplicity 161 Germ, elliptic 82 Germ, elliptic map, infinitesimally stable 155 Germ, elliptic map, stable 149 Germ, finitely determined (finite) 150 Germ, hyperbolic 83 Germ, parabolic 82 Germs, equivalence 11 Germs, stable equivalence 12 63 Giblin, P.J. 136 221 224 Gibson, C.G. 161 179 226 227 Givental’, A.B. 98 116 117 127 131 192 203 211 222 227 Golubitsky, M. 168 169 221 227 228 Goryunov, V.V. 9 31 112 114 125 143 161 165 168—170 174 183 217 223 228 Gradient ideal 13 154 Grassmann bundle 188 Greuel, G.M. 94 95 228 Griffiths, P. 97 106 108 228 Gromov, M.L. 201 214—215 228 Grothendieck, A. 132 Group complex-monodromy 90 Group of quasijets of diffeomorphisms 41 Group, braid 65 124 Group, Coxeter 119 Group, geometric 172 Group, monodromy 56 58 69 Group, nice geometric 173 Group, unipotent 175 Group, Weyl 127 Gudkov, D.A. 118 228 Guillemin, V. 221 227 Gunning, R.C. 91 93 228 Guse 18 20 33 62 63 70—72 83 101 117 119 130 132 151 161 163 221 223 228 229 Gysin homomorphism 190 h-principle 214 Haefliger, A. 186 187 223 229 Harris, J. 106 228 Hartman, P. 96 229 Hartshorne, R. 134 175 229 Herv 93 229 Hironaka, H. 103 229 Hirsch, M. 213 214 229 Hodge filtration 106 107 Hodge filtration, asymptotic 108 Hodge filtration, pure 106 Hodge number 111 Hodge structure, mixed 106 Homomorphism of DA algebras 170 Homomorphism of formal algebras 170 Homomorphism of formal algebras, Lagrangian 215 Homomorphism of modules over a system of rings 171 Homomorphism of tangent bundles 213 Homotopy, admissible 74 Homotopy, smooth 74 Hung, N.H.V. 145 229 Husemoller, D. 138 142 229 Hyperbolic singularity 83 Ideal, gradient 13 154 Ideal, primitive 169 Igusa, K. 216 229 Il’yashenko, Yu.S. 222 Immersion 190 Immersion, Lagrangian 192 Infmitesimally versal deformation 17 168 Intersection form of a section 101 Intersection index 192 Intersection matrix of a singularity 61 Intrinsic modality 45 Ivlev, B.M. 40 Jacobian extension 154 Janssen, W. 88 229 Jaworski, P. 8 135—138 229 jet 14 150 Jet space 151 Jet, sufficient 14 150 Join 75 K 105 Kapranov, M.M. 219 229 Katz, N. 97 229 Kempf, G. 103 229 Khimshiashvili, G.N. 164 229 Khovanski 8 103 104 112 163—165 223 225 229 Kleiman, S.L. 203 217 230 Klein, F. 26 230 Kneser, M. 86 230 Knudsen, F. 103 229 Kodaira, K. 30 Kosinski, A. 186 187 229 Kulikov, V.S. 30 32 217 230 Kuo, T.C. 183 230 Kushnirenko, A.G. 39 104 115 161 163 230 Lada, T.J. 140 225 Lagrangian immersion (manifold) 192 Lamotke, K. 62 230 Lander, L. 221 224 Landis, E.E. 153 230 Laplace, P.S. 7 Lashof, R.K. 140 226 Lazzeri, F. 21 36 62 70 230 Le, D.T. 70 230 Lees, J.A. 214 215 230 Lefschetz, S. 51 56 59 230 Leray, J. 92 230 Level bifurcation set 19 Level set, nonsingular 51 Levine, H. 164 191 212 226 230 Lin, V.Ya 140 230 Lipman, J. 27 230 Local algebra of a map 38 157 Local algebra of a singularity 13 Looijenga, E.J.N. 86 100 130 132 135 179 182 227 230 Luengo, I. 71 230 Luna, D. 171 230 Lyashko, O.V. 8 9 68 127 132 133 161 165 168—170 174 183 217 223 231 Mac Lane, S. 47 231 Malgrange, B. 91 92 97 170 171 231 Manin, Yu.I. 89 231 Map, infmitesimally stable 155 167 Map, Maurin 191 Map, nondegenerate quasihomogeneous 38 Map, period 91 Map, quasihomogeneous 38 Map, semi-guasihomogeneous 39 184 Map, smooth 148
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