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

@article{Stumpf1999ChaoticBI, title={Chaotic behaviour in the newton iterative function associated with kepler's equation}, author={L. Stumpf}, journal={Celestial Mechanics and Dynamical Astronomy}, year={1999}, volume={74}, pages={95-109} }

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.

## 15 Citations

The dynamics of Kepler equation

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- 2003

It is well known that Kepler?s equation can be solved by means of an iterative
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- 2016

Abstract In this article, a simple approach is suggested to calculate the approximate dates of opposition and conjunction of Earth and Mars since their opposition on August 28, 2003 (at perihelion of…

Chaotic Behavior in the Real Dynamics of a One Parameter Family of Functions

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- 2014

The chaotic behavior in the real dynamics of a one parameter family of nonlinear functions is studied in the present paper. For this purpose, the function f_λ(x)=λ=xe^x /( x - 1) λ ＞ 0, x ∈ R \ {1}…

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