Asian Journal of Mathematics

Volume 14 (2010)

Number 3

Genericity of Caustics and Wavefronts on an r-corner

Pages: 335 – 358

DOI: http://dx.doi.org/10.4310/AJM.2010.v14.n3.a4

Author

Takaharu Tsukada

Abstract

We investigate genericities of reticular Lagrangian maps and reticular Legendrian maps in order to give generic classifications of caustics and wavefronts generated by a hypersurface germ without or with a boundary in a smooth manifold. We also give simpler proofs of main results in T. Tsukada, "Reticular Lagrangian Singularities," Asian J. Math., 1 (1997), pp. 572-622 and T. Tsukada, "Reticular Legendrian Singularities," Asian J. Math., 5:1 (2001), pp. 109-127.

Keywords

Caustic; wavefront; r-corner; stability; genericity

2010 Mathematics Subject Classification

53Dxx, 58K25

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