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Physicists’ Treatment of Catastrophes Before Catastrophe Theory

Chapter
Part of the Encyclopaedia of Mathematical Sciences book series (volume 5)

Abstract

Physicists have always made use of constructions more or less equivalent to catastrophe theory in investigations of concrete problems. In this sense, catastrophe theory may be compared with mathematical analysis. Without the help of analysis, Huygens was able to solve the majority of problems solved by Newton. But such solutions required the genius of Huygens while, nowadays, the same problems may be solved with the help of analysis by any student. In exactly the same way, mastery of the technique of singularity theory allows one to obtain results automatically that otherwise require inventiveness and substantial efforts of imagination, simultaneously extending them to more complicated situations where “elementary” methods would lead to vast calculations. (1974) in an article “Nobel prizes for catastrophes” points out many examples of acknowledged physical achievements, whose authors, independently of one another, used ideas formalized later in singularity theory.

Keywords

Bifurcation Diagram Thermal Explosion Catastrophe Theory Legendre Transformation Versal Deformation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteMoscowRussia

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