Singularities, bifurcations, and catastrophes

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'').

PACS: 02.30.−f, 03.40.Kf
DOI: 10.1070/PU1983v026n12ABEH004581
URL: https://ufn.ru/en/articles/1983/12/a/
Citation: Arnol’d V I "Singularities, bifurcations, and catastrophes" Sov. Phys. Usp. 26 1025–1037 (1983)

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%0 Journal Article
%T Singularities, bifurcations, and catastrophes
%A V. I. Arnol’d
%I Physics-Uspekhi
%D 1983
%J Phys. Usp.
%V 26
%N 12
%P 1025-1037
%U https://ufn.ru/en/articles/1983/12/a/
%U https://doi.org/10.1070/PU1983v026n12ABEH004581

Оригинал: Арнольд В И «Особенности, бифуркации и катастрофы» УФН 141 569–590 (1983); DOI: 10.3367/UFNr.0141.198312a.0569