From: "Arne Dehli Halvorsen" <adh@computas.no>
Subject: Re: Any Ideas Guys & Gals (Course Project)
Date: Thu, 8 Apr 1999 09:35:34 +0200
Newsgroups: sci.math
Keywords: chaotic dynamical systems with symmetries

Here's one I would have liked to do myself, but I understand that before
 I get down to it, this stuff will probably be old hat.

Julien Clinton Sprott (http://sprott.physics.wisc.edu/sprott.htm) at U. of
Wisconsin has run an automated search for chaotic dynamical systems,
 using Basic programs that he has placed on his home page.  He has
tried to find the simplest chaotic attractors in 3-d, and has succeded in
finding very simple ones, which he has described in publications and in
technical notes on his web page.
http://sprott.physics.wisc.edu/simpjerk.htm

Noticing that the well-known Lorenz attractor has a 2-fold rotational
symmetry, and wondering whether there might be a 3-fold one out there, w
e both searched for such a beast, and several were found:
 http://sprott.physics.wisc.edu/chaos/symmetry.htm

(The 2-fold symmetric one is invariant under this transformation:
x:= -x
y:=-y
z := z
The 3-fold one is invariant under:
x:=y
y:=z
z:=x)


The project:  Can simple chaotic attractors be found in 3-d with other
interesting symmetries?
Restricted two first degree equations with quadratic nonlinearities in 3-d,
this should be feasible.

Let me know if you try this out,

Arne D Halvorsen



JesseJenna wrote in message <19990407232111.24974.00000867@ng23.aol.com>...
>Hello,
>        I am a junior mathematics major at a liberal arts college in
kentucky
>(Berea College).  I am currently taking a computer science course in which
we
>get to do a final project (language is C++)....  I have had many csc
classes
>before, and I had done things in 3d, sound, etc, but I want to do something
>with math research for the final project in this class.  Does anyone know
of
>any cool topics which research could be done on and work on the computer
side
>also....  Any ideas would be greatly appreciated, as right now all I can
think
>of is the 4 color theorem.
>
>Jesse Andrews
>jessejenna@aol.com