The Theory of Singularities and its Applications
The Theory of Singularities and its Applications
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奇点理论及其应用
DOI：
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发表时间：
1991
期刊：
影响因子：
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通讯作者：
V. I. Arnolʹd
中科院分区：
文献类型：
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作者：
V. I. Arnolʹd
第一部分.奇异动物园：1。莫尔斯函数论2.惠特尼映射理论3. 4.第四把雨伞第五章.反射群的判别式6.二十面体与避障问题7。展开的燕尾服8.折叠和打开的雨伞9.投影的奇异性和表观轮廓的奇异性第二部分。分叉图的奇异性：10。函数族的分叉图11.稳定边界12.椭圆边界和最小值函数13. 14.第十四章不共轭方程，切比雪夫系统边界和舒伯特奇异性在旗流形15。格拉斯曼流形中的基本系统边界、射影曲线环和舒伯特奇点。
Part I. The Zoo of Singularities: 1. Morse theory of functions 2. Whitney theory of mappings 3. The Whitney-Cayley umbrella 4. The swallowtail 5. The discriminants of the reflection groups 6. The icosahedron and the obstacle by-passing problem 7. The unfurled swallowtail 8. The folded and open umbrellas 9. The singularities of projections and of the apparent contours Part II. Singularities of Bifurcation Diagrams: 10. Bifurcation diagrams of families of functions 11. Stability boundary 12. Ellipticity boundary and minima functions 13. Hyperbolicity boundary 14. Disconjugate equations, Tchebyshev system boundaries and Schubert singularities in flag manifolds 15. Fundamental system boundaries, projective curve flattenings and Schubert singularities in Grassmann manifolds.