Lagrangian and Legendrian singularities. (English. Russian original) Zbl 0331.58007
Funct. Anal. Appl. 10, 23-31 (1976); translation from Funkts. Anal. Prilozh. 10, No. 1, 26-36 (1976).
MSC:
| 37J99 | Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems |
| 58D05 | Groups of diffeomorphisms and homeomorphisms as manifolds |
| 58A05 | Differentiable manifolds, foundations |
References:
| [1] | J. Guckenheimer, ”Catastrophes and partial differential equations,” Ann. Inst. Fourier,23, No. 2, 31-59 (1973). · Zbl 0271.35006 |
| [2] | V. I. Arnol’d, ”Normal forms of functions near degenerate critical points, the Weyl groups of Ak, Dk, Ek, and Lagrangian singularities,” Funktsional’. Analiz i Ego Prilozhen.,6, No. 4, 3-25 (1972). |
| [3] | L. Hörmander, ”Fourier integral operators. I,” Acta Math.,127, 79-183 (1971). · Zbl 0212.46601 · doi:10.1007/BF02392052 |
| [4] | V. I. Arnol’d, Mathematical Methods of Classical Mechanics [in Russian], Nauka, Moscow (1974). |
| [5] | V. M. Zakalyukin, ”The versality theorem,” Funktsional’. Analiz i Ego Prilozhen.,7, No. 2, 28-31 (1973). |
| [6] | D. Mazer, ”Stability of C? mappings. III,” Matematika,14, No. 1, 145-175 (1970). |
| [7] | F. Latur, ”Stabilité des champs d’applications differentiables,” C. R. Acad. Sci. (Paris),268, 1331-1334 (1969). |
| [8] | V. I. Arnol’d, ”Classification of unimodal critical points of functions,” Funktsional’. Analiz i Ego Prilozhen.,7, No. 3, 75-77 (1973). |
| [9] | V. I. Arnol’d, ”Classification of bimodal critical points of functions,” Funktsional’. Analiz i Ego Prilozhen.,9, No. 1, 49-51 (1975). |
| [10] | A. Weinstein, ”Lagrangian manifolds,” Adv. Math.,6, 347-410 (1971). · Zbl 0213.48203 · doi:10.1016/0001-8708(71)90020-X |
| [11] | J. Guckenheimer, ”Caustics and nondegenerate Hamiltonians,” Topology,13, 127-133 (1974). · Zbl 0291.58010 · doi:10.1016/0040-9383(74)90003-2 |
| [12] | A. Weinstein, ”Lagrangian submanifolds and Hamiltonian systems,” Ann. Math.,98, 377-410 (1973). · Zbl 0271.58008 · doi:10.2307/1970911 |
| [13] | K. Jänich, ”Caustics and catastrophes,” Math. Ann.,209, 161-180 (1974). · doi:10.1007/BF01351319 |
| [14] | M. Golubitsky, Contact Equivalence for Lagrangian Manifolds, Lecture Notes in Math., No. 468 (1975), pp. 71-73. · Zbl 0295.57018 · doi:10.1007/BFb0082605 |
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