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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/158 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/158 http://eprints.org/relation/isCoversheetVersionOf https://pure.iiasa.ac.at/id/document/158 archive 351 disk0/00/00/01/79 2016-01-15 01:41:05 2021-08-27 17:07:34 2016-01-15 01:41:05 monograph show 2 Casti J.L. 974 pub iis_met prog_sds Recently, a new mathematical tool called "catastrophe theory" has been developed by the topologists Thom, Zeeman, Mather, and others in an attempt to mathematically explain the discontinuities of observed behavior due to smooth changes in the basic parameters of physical, social, and biological processes. It has been shown that the number of mathematically distinct ways in which such discontinuities may arise is small when compared with the dimension of the process, and a complete classification of all distinct types has been made for processes depending upon five or less parameters. The purpose of this note is two-fold: first, to serve as a very brief introduction to the subject of catastrophe theory and secondly, to illustrate the theory by applying it to the determination of equilibrium configurations for stellar matter which has reached the endpoint of thermonuclear evolution, the problem of "stellar collapse". It will be seen that catastrophe theory enables us to give a very satisfactory explanation for the observed phenomenon of unstable equilibrium configurations and the appearance of the so-called Chandrasekhar and Oppenheimer-Landau-Volkoff crushing points. 1974-12 published RM-74-028 RM-74-028 10 1179 public research_memorandum IIASA, Laxenburg, Austria 14 FALSE info:eu-repo/semantics/book