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Lagrangian manifolds with singularities, asymptotic rays, and the open swallowtail. (English) Zbl 0487.58003


MSC:

58C25 Differentiable maps on manifolds
58K99 Theory of singularities and catastrophe theory
58E30 Variational principles in infinite-dimensional spaces
70H99 Hamiltonian and Lagrangian mechanics
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems

Citations:

Zbl 0484.58008
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Full Text: DOI

References:

[1] R. B. Melrose, ”Equivalence of glancing hypersurfaces,” Invent. Math.,37, No. 3, 165-192 (1976). · Zbl 0354.53033 · doi:10.1007/BF01390317
[2] H. Whitney, ”On singularities of mappings of Euclidean spaces. I,” Ann. Math.,62, 374-410 (1955). · Zbl 0068.37101 · doi:10.2307/1970070
[3] B. Morin, ”Formes canoniques des singularités d’une application differentiable,” C. R. Acad. Sci., Paris,260, 5662-5665, 6503-6506 (1965). · Zbl 0178.26801
[4] V. I. Arnol’d, ”Indices of singular points of 1-forms on a manifold with boundary, displacement of invariants of groups, generated by reflections, and singular projections of smooth surfaces,” Usp. Mat. Nauk,34, No. 2, 3-38 (1979).
[5] V. I. Arnold, ”Wave fronts evolution and equivariant Morse lemma,” Commun. Pure Appl. Math.,28, No. 6, 557-582 (1976). · Zbl 0343.58003 · doi:10.1002/cpa.3160290603
[6] L. Solomon, ”Invariants of finite reflection groups,” Nagoya Math. J.,22, 57-64 (1963). · Zbl 0117.27104
[7] V. I. Arnol’d, Ergodic Problems of Classical Mechanics, W. A. Benjamin (1968).
[8] O. V. Lyashko, ”Geometry of bifurcation diagrams,” Usp. Mat. Nauk,34, No. 4, 205-206 (1979). · Zbl 0434.32020
[9] O. A. Platonova, ”Singularities in the problem of circuit of an obstruction,” Funkts. Anal. Prilozhen.,15, No. 2, 86-87 (1981). · Zbl 0464.58009
[10] V. I. Arnol’d, Ya. B. Zel’dovich, and S. F. Shandarin, ”Elements of the large-scale structure of the Universe,” Usp. Mat. Nauk,36, No. 3, 244-245 (1981).
[11] V. I. Arnol’d, ”Covering of a caustic by the cuspidal edge of a moving front,” Usp. Mat. Nauk,36, No. 4, 233 (1981).
[12] L. Euler, Introductio in Analysin Infinitorum, Lausanne, Bosquet, No. 316 (1748). · Zbl 0096.00302
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