bifurcation sets
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6 matching pages
1: 36.4 Bifurcation Sets
§36.4 Bifurcation Sets
… ► , fold bifurcation set: … ► , cusp bifurcation set: … ► , swallowtail bifurcation set: … ►§36.4(ii) Visualizations
…2: 36.15 Methods of Computation
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►Far from the bifurcation set, the leading-order asymptotic formulas of §36.11 reproduce accurately the form of the function, including the geometry of the zeros described in §36.7.
Close to the bifurcation set but far from , the uniform asymptotic approximations of §36.12 can be used.
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3: 36.5 Stokes Sets
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►The Stokes set is itself a cusped curve, connected to the cusp of the bifurcation set:
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►They generate a pair of cusp-edged sheets connected to the cusped sheets of the swallowtail bifurcation set (§36.4).
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►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.
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►In Figure 36.5.4 the part of the Stokes surface inside the bifurcation set connects two complex saddles.
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4: 36.14 Other Physical Applications
5: 36.7 Zeros
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►Deep inside the bifurcation set, that is, inside the three-cusped astroid (36.4.10) and close to the part of the -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.
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