A class of Lorenz-type systems, their factorizations and extensions

It is well known that the Lorenz system has $Z_2$-symmetry. Using introducted in math.DS/0105147 topological covering-coloring a new representation for the Lorenz system is obtained. Deleting coloring leads to the factorized Lorenz system that is in a sense more fundamental than the original one. Finally, $Z_n$ extensions define a class of Lorenz-type systems. The approach admits a natural generalization for regular and chaotic systems with arbitrary symmetries.