Chaotic behaviour in the newton iterative function associated with Kepler's equation

The chaotic behaviour observed when Newton's method is used to solve Kepler 's equation is analysed using methods borrowed from chaos theory. The resul t of the analysis is compared with previous results. A sufficient condition for convergence of a given iterative function is presented and yields rang es of eccentricity and mean anomaly such that Newton's method applied to Ke pler's equation will converge from an initial guess of pi.