The theories of smooth-mapping singularities and dynamical-system bifurcations are reviewed. Mention is made of the applications to optics (caustic and wave-front metamorphoses) and to theories of short-wave asymptotics, the origin of large-scale structure in the universe, and loss of equilibrium and self-oscillation stability (``catastrophe theory'').

@article{Arnol’d:1983,
	author = {V. I. Arnol’d},
	title = {Singularities, bifurcations, and catastrophes},
	publisher = {Physics-Uspekhi},
	year = {1983},
	journal = {Phys. Usp.},
	volume = {26},
	number = {12},
	pages = {1025-1037},
	url = {https://ufn.ru/en/articles/1983/12/a/},
	doi = {10.1070/PU1983v026n12ABEH004581}
}