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1: 36.2 Catastrophes and Canonical Integrals
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Normal Forms Associated with Canonical Integrals: Cuspoid Catastrophe with Codimension
… ►Special cases: , fold catastrophe; , cusp catastrophe; , swallowtail catastrophe. ►Normal Forms for Umbilic Catastrophes with Codimension
… ►Canonical Integrals
… ►Diffraction Catastrophes
…2: 36.4 Bifurcation Sets
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Bifurcation (Catastrophe) Set for Cuspoids
… ►Bifurcation (Catastrophe) Set for Umbilics
… ► , fold bifurcation set: … ► ► …3: 36.7 Zeros
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Table 36.7.1: Zeros of cusp diffraction catastrophe to 5D.
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►The zeros of these functions are curves in space; see Nye (2007) for and Nye (2006) for .
§36.7(i) Fold Canonical Integral
… ►Zeros inside, and zeros outside, the cusp . | |||||
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4: 36.6 Scaling Relations
5: 36.10 Differential Equations
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, fold: (36.10.1) becomes Airy’s equation (§9.2(i))
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36.10.3
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, fold: (36.10.6) is an identity.
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6: 36.5 Stokes Sets
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►Stokes sets are surfaces (codimension one) in space, across which or acquires an exponentially-small asymptotic contribution (in ), associated with a complex critical point of or .
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7: 21.8 Abelian Functions
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►An Abelian function is a -fold periodic, meromorphic function of complex variables.
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