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cusp bifurcation set


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1: 36.4 Bifurcation Sets
K = 2 , cusp bifurcation set: … Elliptic umbilic bifurcation set (codimension three): for fixed z , the section of the bifurcation set is a three-cusped astroid …
§36.4(ii) Visualizations
See accompanying text
Figure 36.4.1: Bifurcation set of cusp catastrophe. Magnify
2: 36.5 Stokes Sets
The Stokes set is itself a cusped curve, connected to the cusp of the bifurcation set: … They generate a pair of cusp-edged sheets connected to the cusped sheets of the swallowtail bifurcation set36.4). … This consists of three separate cusp-edged sheets connected to the cusp-edged sheets of the bifurcation set, and related by rotation about the z -axis by 2 π / 3 . … This consists of a cusp-edged sheet connected to the cusp-edged sheet of the bifurcation set and intersecting the smooth sheet of the bifurcation set. …
3: 36.7 Zeros
Deep inside the bifurcation set, that is, inside the three-cusped astroid (36.4.10) and close to the part of the z -axis that is far from the origin, the zero contours form an array of rings close to the planes …Outside the bifurcation set (36.4.10), each rib is flanked by a series of zero lines in the form of curly “antelope horns” related to the “outside” zeros (36.7.2) of the cusp canonical integral. …