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

Stumpf, L and Kormos, Laura (1999) Chaotic behaviour in the newton iterative function associated with Kepler's equation. Celestial Mechanics and Dynamical Astronomy, 74 (2). pp. 95-109. ISSN 0923-2958

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Abstract

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 pi.

Item Type: Article
Journal or Publication Title: Celestial Mechanics and Dynamical Astronomy
Uncontrolled Keywords: Kepler's equation ; Schwarzian derivative ; Newton's method
Subjects:
Departments: Faculty of Science and Technology > Physics
ID Code: 52343
Deposited By: ep_importer_pure
Deposited On: 23 Jan 2012 09:05
Refereed?: Yes
Published?: Published
Last Modified: 09 Apr 2014 23:01
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/52343

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