Dear Don:

I must admit my lack of experience in modern nonlinear mathematics and physics. The field you may want to absorb appears to me so vast that any unprofessional advice is bound to result in random and lengthy meandering. While there is a couple of books I am aquaintant with and suspect may be useful, I would seek out somebody who is more directly involved with the current develpments. I would certainly post a question to the sci.math newsgroup. The two books I have in mind are these:

M. Schroeder, Fractals, Chaos, Power Laws, W. H. Freeman & Co., 1991
Les Relations Entre les Mathématiques et la Physique Théorique, IHES, 1998

Far as I can judge, your idea of matter and antimatter having different orientations in a higher dimensional space appears to me sensibly reasonable.

I wish you all the success,
Alexander Bogomolny