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.
Read more about this topic: Catastrophe Theory
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Here leave us to die out with these
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—Matthew Arnold (1822–1888)