Abstract
A principally new treatment of caustics as catastrophes has been a relatively recent proposition, but the significance of this innovation could hardly be overestimated. The new approach has allowed one to classify caustics, to select among them structurally stable species, and to establish a subordinance for caustics of different complexity. It has been the historically first breakthrough to understanding the nature of caustics.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
V.P. Maslov: Théorie des Perturbations et Méthode Asymptotique (Dunod, Paris 1972)
A.A. Andronov, A.A. Vitt, S.E. Haikin: Teoriya Kolebanii (theorie of oscillations) (Nauka, Moscow 1981)
V.I. Arnold: Usp. Mat. Nauk 23, 3 (1968); 29, 11, 243 (1974); ibid. 30, 560 (1975)
R. Thorn: Structural Stability and Morphogenesis (Benjamin, New York 1975)
T. Poston, N. Stewart: Catastrophe Theory and its Applications (Pitman, London 1978)
M. Golubitsky, V. Guillimin: Stable Mappings and Their Singularities, Graduate Texts Math., Vol. 14(Springer, Berlin, Heidelberg 1973)
R. Gilmor: Catastrophe Theory for Scientists and Engineers (Wiley, New York 1981)
J.J. Dustermaat: Commun. Pure Appl. Math. 27, 207 (1974)
V.I. Arnold, A.N. Varchenko, S.M. Gussein-Zade: Singularities of Differentiale Mappings, Vols. 1, 2 (Birkhäuser, Boston 1985, 1988)
V.I. Arnold: Sov. Phys.-Usp. 26, 1024 (1983)
V.I Arnold: Catastrophe Theory, 3rd edn. (Spinger, Berlin, Heidelberg 1992)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Kravtsov, Y.A., Orlov, Y.I. (1993). Caustics as Catastrophes. In: Caustics, Catastrophes and Wave Fields. Springer Series on Wave Phenomena, vol 15. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-97491-5_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-97491-5_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-97493-9
Online ISBN: 978-3-642-97491-5
eBook Packages: Springer Book Archive