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Catastrophe theory

From Academic Kids

Catastrophe theory is a branch of mathematics that deals with dynamical systems and was originated with the work of the French mathematician René Thom in the 1960s. It studies and classifies phenomena characterized by sudden shifts in behavior arising from small changes in circumstances, analysing how the qualitative nature of equation solutions depends on the parameters that appear in the equation. For example, in a landslide, the timing and magnitude are seemingly unpredictable.

Bibliographical references

  • Arnold, Vladimir Igorevich. Catastrophe Theory, 3rd ed. Berlin: Springer-Verlag, 1992.
  • Gilmore, Robert. Catastrophe Theory for Scientists and Engineers. New York: Dover, 1993.
  • Poston, T. and Stewart, Ian. Catastrophe: Theory and Its Applications. New York: Dover, 1998.
  • Sanns, Werner. Catastrophe Theory with Mathematica: A Geometric Approach. Germany: DAV, 2000.
  • Saunders, Peter Timothy. An Introduction to Catastrophe Theory. Cambridge, England: Cambridge University Press, 1980.
  • Thom, René. Structural Stability and Morphogenesis: An Outline of a General Theory of Models. Reading, MA: Addison-Wesley, 1989.
  • Thompson, J. Michael T. Instabilities and Catastrophes in Science and Engineering. New York: Wiley, 1982.
  • Woodcock, Alexander Edward Richard and Davis, Monte. Catastrophe Theory. New York: E. P. Dutton, 1978.
  • Zeeman, E.C. Catastrophe Theory-Selected Papers 1972-1977. Reading, MA: Addison-Wesley, 1977.

See also

Broken symmetry, tipping point, phase transition, domino effect, snowball effect, Butterfly effect, spontaneous symmetry breaking, Singularity theory.

External links

Catastrophe Theory: CompLexicon [1] (http://www.exploratorium.edu/complexity/CompLexicon.html) Template:Maths-stubde:Katastrophentheorie pl:Teoria katastrof

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