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Singularities of Legendre varieties, of evolvents and of fronts at an obstacle

Published online by Cambridge University Press:  19 September 2008

V. I. Arnol'd
V. I. Arnol'd
Affiliation:
Department of Mathematics and Mechanics, Moscow State University, Lenin Hills 117234, Moscow, USSR
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Abstract

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The Legendre manifolds are the maximal integral submanifolds of a contact manifold. The shortest path problem on a manifold with boundary leads to Legendre varieties. We find normal forms of their generic singularities in terms of binary forms invariants theory.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 2 , Issue 3-4 , December 1982 , pp. 301 - 309
Copyright
Copyright © Cambridge University Press 1982

References

REFERENCES

[1]Platonova, O. A.. Singularities in the shortest way problem at an obstacle. Funct. Anal. 15 (1981), 86–87.Google Scholar
[2]Arnol'd, V. I. Catastrophes theory. Znanie: Moscow, 1981. (In Russian.)Google Scholar
[3]Arnol'd, V. I.. Evolution of singularities of potential flows in collision free media and caustics metamorphosae in 3-space. Trudy semin. im. I. G. Petrovskogo 8 (1982), 21–57. (In Russian.)Google Scholar
[4]Arnol'd, V. I.. Lagrange varieties, asymptotical rays and the open swallowtail. Funct. Anal. 15 (1981), 1–14.Google Scholar
[5]Guivental, A. B.. Varieties of polynomials having a prescribed multiplicity root and the generalized Newton equation. Fund. Anal. 16 (1982), 8–13.Google Scholar
[6]Arnol'd, V. I.. Mathematical Methods of Classical Mechanics. Springer: New York, 1978.CrossRefGoogle Scholar
[7]Arnol'd, V. I., Varchenko, A. N. & Gusein-Zade, S. M.. Singularities of Differentiable Mappings. Nauka: Moscow, 1982. (In Russian.)Google Scholar