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Issue 12, 2025
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Reviews of topical problems


Singularities, bifurcations, and catastrophes


V.A. Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russian Federation

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'').

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Fulltext is also available at DOI: 10.1070/PU1983v026n12ABEH004581
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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Оригинал: Арнольд В И «Особенности, бифуркации и катастрофы» УФН 141 569–590 (1983); DOI: 10.3367/UFNr.0141.198312a.0569

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