#### MTd2

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http://en.wikipedia.org/wiki/Catastrophe_theory

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http://en.wikipedia.org/wiki/Catastrophe_theory

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Hi MTd2! Are you any relation of R2d2?

http://en.wikipedia.org/wiki/Catastrophe_theory

As I expect you found, the A,D,E classification of catastrophes by names beginning with A D and E makes the As correspond to the A series of Lie groups, the Ds to the D series, and the Es to the E series … http://en.wikipedia.org/wiki/ADE_classification

In turn, the A series of Lie groups correspond to SU groups, and the B series to SL groups.

There are also C and D series of Lie groups (not connected with catastrophes), and finally the E F and G series, officially known as "exceptional" cases … http://en.wikipedia.org/wiki/Simple_Lie_group#Infinite_series

so I guess the E

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Well, people used to call me R2D2 at college! But that's because I use a wheelchair! :rofl: :rofl: :rofl:

Now, seriously, I am asking somthing a little bit different. According to this list provided in the wiki (http://en.wikipedia.org/wiki/Catastrophe_theory): [Broken]

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

* A0 - a non-singular point: V = x.

* A1 - a local extrema, either a stable minimum or unstable maximum V = \pm x^2 + a x.

* A2 - the fold

* A3 - the cusp

* A4 - the swallowtail

* A5 - the butterfly

* Ak - an infinite sequence of one variable forms V=x^{k+1}+\cdots

* D4- - the elliptical umbilic

* D4+ - the hyperbolic umbilic

* D5 - the parabolic umbilic

* Dk - an infinite sequence of further umbilic forms

* E6 - the symbolic umbilic V = x3 + y4 + axy2 + bxy + cx + dy + ey2

* E7

* E8

//////

There is just one exceptional explained, but I couldn't find the other 2. I'd like to know what is the stable polynomial of the other 2 Es as well as its sketched behavior.

Now, seriously, I am asking somthing a little bit different. According to this list provided in the wiki (http://en.wikipedia.org/wiki/Catastrophe_theory): [Broken]

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

* A0 - a non-singular point: V = x.

* A1 - a local extrema, either a stable minimum or unstable maximum V = \pm x^2 + a x.

* A2 - the fold

* A3 - the cusp

* A4 - the swallowtail

* A5 - the butterfly

* Ak - an infinite sequence of one variable forms V=x^{k+1}+\cdots

* D4- - the elliptical umbilic

* D4+ - the hyperbolic umbilic

* D5 - the parabolic umbilic

* Dk - an infinite sequence of further umbilic forms

* E6 - the symbolic umbilic V = x3 + y4 + axy2 + bxy + cx + dy + ey2

* E7

* E8

//////

There is just one exceptional explained, but I couldn't find the other 2. I'd like to know what is the stable polynomial of the other 2 Es as well as its sketched behavior.

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I don't know too much about this myself, but I found http://www.math.purdue.edu/~agabriel/dynkin.pdf" [Broken] which gives the singularities corresponding to E6, E7, E8 (for analytic functions C^3->C). You probably want to check the source cited there (particularly [1] by Arnold) for more info.

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x^4 + y^3 + z^2, is more complete on wikipedia, because it has the full stable form with 5 control parameters. I said above that this one was explained, well, sorry. It wasn't, except for expliciting the 5 parameters.

But there is nothing for the other groups. And I checked Arnold's book, in the end, and it is just explained in a very sketchy way the icosahedron/dodecahedron group. I'd like something more complete.

[tex]x^3+xy^3+z^2[/tex]

has a universal unfolding ("stable form")

[tex]x^3+xy^3+z^2+ax+bx^2+cy+dy^2+exy+fx^2y[/tex].

The codimension 7 singularity

[tex]x^3+y^5+z^2[/tex]

has a universal unfolding

[tex]x^3+y^5+z^2+ax+by+cy^2+dy^3+exy+fxy^2+gxy^3[/tex].

Also note that [1] in the link I gave is not Arnold's book but an article in Functional Analysis and Applications.

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Yes, but I can't get that article.

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Hmm, Thank you!

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