hyperbolic umbilic catastrophe
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… ►Define a mapping by relating to the normal form (36.2.1) of in the following way: …with the functions and determined by correspondence of the critical points of and . … ►This technique can be applied to generate a hierarchy of approximations for the diffraction catastrophes in (36.2.10) away from , in terms of canonical integrals for . For example, the diffraction catastrophe defined by (36.2.10), and corresponding to the Pearcey integral (36.2.14), can be approximated by the Airy function when is large, provided that and are not small. … ►For further information concerning integrals with several coalescing saddle points see Arnol’d et al. (1988), Berry and Howls (1993, 1994), Bleistein (1967), Duistermaat (1974), Ludwig (1966), Olde Daalhuis (2000), and Ursell (1972, 1980).