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

  title={Chaotic behaviour in the newton iterative function associated with kepler's equation},
  author={L. Stumpf},
  journal={Celestial Mechanics and Dynamical Astronomy},
  • L. Stumpf
  • Published 1 June 1999
  • Mathematics
  • Celestial Mechanics and Dynamical Astronomy
The chaotic behaviour observed when Newton's method is used to solve Kepler's equation is analysed using methods borrowed from chaos theory. The result of the analysis is compared with previous results. A sufficient condition for convergence of a given iterative function is presented and yields ranges of eccentricity and mean anomaly such that Newton's method applied to Kepler's equation will converge from an initial guess of π. 
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