Résumé: Complex numbers are rede .ned from the plane to two non- Euclidean geometries, namely the surfaces of the sphere and the torus. The properties of the iterated equation zn ? 1 ¼z p n ? c are investigated in these geometries, where z ; p and c are complex numbers. Plots of the number of iterations required by this equation for convergence to a .xed point appear fractal and resemble multiple copies ( at di .erent scales) of the Julia set obtained when the same equation is iterated in the complex plane.

Langue: Anglais