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

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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Published 5 April 2012