Chaotic Root-Finding for a Small Class of Polynomials
Max Little, Daniel Heesch
Abstract
In this paper we present a new closed-form solution to a chaotic difference equation, y(n+1) = a2 y(n)2 + a1 y(n) + a0 with coefficient a0 = (a1 - 4)(a1 + 2) / (4 a2) and using this solution, show how corresponding exact roots to a special set of related polynomials of order 2p, p in the naturals, with two independent parameters can be generated, for any p.
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