Literature Cited
V. I. Arnol'd, "Characteristic class which occurs in the quantization condition," Funkts. Anal. Prilozhen.,1, No. 1, 1–14 (1967).
V. I. Arnol'd, "Singularities of system of rays," Usp. Mat. Nauk,38, No. 2, 77–147 (1983).
V. I. Arnol'd, A. N. Varchenko, and S.-M. Gusein-Zade, Singularities of Differentiable Maps [in Russian], Vol. 1, Nauka, Moscow (1984).
O. P. Shcherbak, "Projective duality of spaces curves and Legendre singularities," Trudy Tbilis. Univ.,232–233, Nos. 13–14, 280–336 (1982).
M. Gromov, "Pseudo holomorphic curves in symplectic manifolds," Invent. Math.,82, No. 5, 307–347 (1985).
H. Whitney, "The general type of singularities of a set of 2n — 1 smooth functions of n variables," Duke J. Math.,45, Ser. 2, 220–293 (1944).
Additional information
Institute of Chemical Physics, Academy of Sciences of the USSR. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 20, No. 3, pp. 35–41, July–September, 1986.
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Givental’, A.B. Lagrangian imbeddings of surfaces and unfolded Whitney umbrella. Funct Anal Its Appl 20, 197–203 (1986). https://doi.org/10.1007/BF01078471
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DOI: https://doi.org/10.1007/BF01078471