Algebraic Geometry of Discrete Dynamics.

[web2k]

http://lanl.arxiv.org/abs/hep-th/0501235

Algebraic Geometry of Discrete Dynamics. The case of one variable
Authors: V.Dolotin, A.Morozov

This paper and related papers at the Los Alamos National archive in the sections for High Energy Physics Theory discuss mathematics of the Mandelbrot and Julia Sets at a level of math I hardly understand.  Hopefully one of the members of this forum can help bridge some of the gaps.

I found his schematics of the structure of the Mandelbrot set quite intriguing.  They relate to my own musing about how to show the scaling invariant nature of the M-set as based on restarting the interations after translation, scaling and rotation of the orign.

In any case, I thought this group should become aware of the work--especially when it is archived in such an unusual place.

Web 2k

[cKleinhuis]

hmm, interesting paper you found there   

as far as i can see they are defining a mathematical way to determine the bifurcation behaviour of a chaotic system, but have only read the introduction yet ...   :