Methods and Applications of Analysis

Volume 18 (2011)

Number 3

Bifurcations of wavefronts on $r$-corners: semi-local classification

Pages: 303 – 334

DOI: http://dx.doi.org/10.4310/MAA.2011.v18.n3.a3

Author

Takaharu Tsukada (Department of Mathematics, Nihon University, Kita-ku, Tokyo, Japan)

Abstract

We introduce the notion of multi-reticular Legendrian unfoldings in order to investigate stabilities and a genericity of bifurcations of wavefronts generated by m points of a hypersurface with a boundary, a corner, or an r-corner in a smooth n dimensional manifold. We define several stabilities of multi-reticular Legendrian unfoldings and prove that they and the stabilities of corresponding generating families are all equivalent and give the classification of all generic bifurcations of their wavefronts in the cases $r = 0, n ≤ 5 and r = 1, n ≤ 3$ respectively.

Keywords

wavefront, bifurcation, Legendrian unfolding, r-corner

2010 Mathematics Subject Classification

53Dxx, 58K25, 58K40

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