Catastrophe Theory - Arnold's Notation

Arnold's Notation

Vladimir Arnold gave the catastrophes the ADE classification, due to a deep connection with simple Lie groups.

  • A0 - a non-singular point: .
  • A1 - a local extremum, either a stable minimum or unstable maximum .
  • A2 - the fold
  • A3 - the cusp
  • A4 - the swallowtail
  • A5 - the butterfly
  • Ak - a representative of an infinite sequence of one variable forms
  • D4- - the elliptical umbilic
  • D4+ - the hyperbolic umbilic
  • D5 - the parabolic umbilic
  • Dk - a representative of an infinite sequence of further umbilic forms
  • E6 - the symbolic umbilic
  • E7
  • E8

There are objects in singularity theory which correspond to most of the other simple Lie groups.

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