Bifurcations of wavefronts on \(r\)-corners: semi-local classification (Q390189)
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scientific article; zbMATH DE number 6249177
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Bifurcations of wavefronts on \(r\)-corners: semi-local classification |
scientific article; zbMATH DE number 6249177 |
Statements
Bifurcations of wavefronts on \(r\)-corners: semi-local classification (English)
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22 January 2014
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The author investigates notions of stability and genericity of bifurcations of wavefronts generated by \(m\) points of a hypersurface with boundary, a corner, or an \(r\)-corner, in a smooth \(n\)-dimensional manifold. Several notions of stability of so-called \textit{multi-reticular Legendrian unfoldings} are defined and proven to be equivalent to the stabilities of corresponding generating families. The classification of all generic bifurcations of wavefronts is given in the cases \(r=0\), \(n\leq 5\) and \(r=1\), \(n\leq 3\) respectively.
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wavefront
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bifurcation
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Legendrian unfolding
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\(r\)-corner
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stability
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