Geodesic
Reconstructions of fronts and caustics depending on a~parameter, and versality of mappings
Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya, Tome 22 (1983), pp. 56-93.

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A survey of results is presented in the problem of describing up to diffeomorphism rearrangements of fronts and caustics in one-parameter families of general position in spaces of low dimension. 
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     author = {V. M. Zakalyukin},
     title = {Reconstructions of fronts and caustics depending on a~parameter, and versality of mappings},
     journal = {Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya},
     pages = {56--93},
     publisher = {mathdoc},
     volume = {22},
     year = {1983},
     language = {ru},
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V. M. Zakalyukin. Reconstructions of fronts and caustics depending on a~parameter, and versality of mappings. Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya, Tome 22 (1983), pp. 56-93. http://geodesic.mathdoc.fr/item/INTD_1983_22_a1/