The theory of singularities and its applications

cover......Page 1
Contents......Page 4
Preface......Page 6
1.1 - Morse theory of functions......Page 8
1.2 - Whitney theory of mappings......Page 13
1.3 - \rThe Whitney-Cayley umbrella......Page 17
1.4 - The swallowtail\r......Page 20
1.5 - The discriminants of the reflection groups\r......Page 24
1.7 - The unfurled swallowtail\r......Page 35
1.8 - The folded and the open umbrellas\r......Page 39
1.9 - The singularities of the projections and of the apparent contours\r......Page 42
2.1 - Bifurcation diagrams of families of functions\r......Page 47
2.2 - Stability boundary\r......Page 55
2.3 - Ellipticity boundary and minima functions\r......Page 56
2.4 - Hyperbolicity boundary\r......Page 59
2.5 - Disconjugate equations, Tchebyshev system boundaries and Schubert singularities in complete flag manifolds\r......Page 60
2.6 - Fundamental system boundaries, projective curve flattenings and Schubert singularities in Grassmann manifolds\r......Page 63
References\r......Page 72
Index\r......Page 74