<atl>Dynamics on the complex sphere and torus

Complex numbers are redefined from the plane to two non-Euclidean geometries, namely the surfaces of the sphere and the torus. The properties of the iterated equation <f>zn+1=znp+c</f> are investigated in these geometries, where <f>z,p</f> and <f>c</f> are complex numbers. Plots of the number of iterations required by this equation for convergence to a fixed point appear fractal and resemble multiple copies (at different scales) of the Julia set obtained when the same equation is iterated in the complex plane. [Copyright &y& Elsevier]