The Convergence of Newton–Raphson Iteration with Kepler's Equation

@article{Charles1997TheCO,
  title={The Convergence of Newton–Raphson Iteration with Kepler's Equation},
  author={E. D. Charles and Jeremy B. Tatum},
  journal={Celestial Mechanics and Dynamical Astronomy},
  year={1997},
  volume={69},
  pages={357-372}
}
Conway (Celest. Mech. 39, 199–211, 1986) drew attention to the circumstance that when the Newton–Raphson algorithm is applied to Kepler's equation for very high eccentricities there are certain apparently capricious and random values of the eccentricity and mean anomaly for which convergence seems not to be easily reached when the starting guess for the eccentric anomaly is taken to be equal to the mean anomaly. We examine this chaotic behavior and show that rapid convergence is always reached… 
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