Complex Dynamics, the Mandelbrot Set, and Newton’s Method — or: On Useless and Useful Mathematics

Dierk Schleicher ()
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Dierk Schleicher: Jacobs University

A chapter in An Invitation to Mathematics, 2011, pp 207-220 from Springer

Abstract: Abstract We discuss the theory of iterated polynomials, which is motivated because it is rich, beautiful, and interesting, but not primarily because it is useful. We then discuss the dynamics of the Newton method for finding roots of smooth functions, which is most useful. And finally, we show that they are closely related, and that work on the useful aspects requires deep knowledge of the ‘useless’ theory. This is an appeal against disintegrating mathematics (or science at large) into ‘useful’ and ‘useless’ parts.

Keywords: Positive Measure; Complex Dynamics; Quadratic Polynomial; Fatou Component; Newton Dynamic (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-19533-4_14

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DOI: 10.1007/978-3-642-19533-4_14

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