Methods and Applications of Analysis
Volume 18 (2011)
Bifurcations of wavefronts on $r$-corners: semi-local classification
Pages: 303 – 334
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.
wavefront, bifurcation, Legendrian unfolding, r-corner
2010 Mathematics Subject Classification
53Dxx, 58K25, 58K40