Unimodal and bimodal germs of functions on a manifold with boundary. (English) Zbl 0576.58007
Translation from Tr. Semin. Im. I. G. Petrovskogo 7, 174-189 (Russian) (1979; Zbl 0497.58005).
MSC:
| 58C25 | Differentiable maps on manifolds |
| 58K99 | Theory of singularities and catastrophe theory |
| 32S05 | Local complex singularities |
| 57R45 | Singularities of differentiable mappings in differential topology |
Keywords:
modality of a map-germ; normal form; adjacency; quasihomogeneous; germ; boundary singularities of smooth functions on a manifold with; boundaryReferences:
| [1] | V. I. Arnol’d, ”Critical points of functions on a manifold with boundary, the simple groups Bk, Ck, F4, and singularities of evolutes,” Usp. Mat. Nauk,33, No. 5, 91–105 (1978). |
| [2] | V. I. Arnol’d, ”Critical points of smooth functions and their normal forms,” Usp. Mat. Nauk,30, No. 5, 3–65 (1975). |
| [3] | V. I. Arnol’d, ”Normal forms of functions in a neighborhood of degenerate critical points,” Usp. Mat. Nauk,29, No. 2, 11–49 (1974). |
| [4] | V. I. Matov, ”Singularities of the maximum function on a manifold with boundary,” in: Trudy Seminara im I. G. Petrovskogo, No. 6, Moscow State Unov. (1980). · Zbl 0474.58002 |
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