The Mathematical Institute, University of Oxford, Eprints Archive

Chaotic root-finding for a small class of polynomials

Little, M. A. and Heesch, D. (2004) Chaotic root-finding for a small class of polynomials. Journal of Difference Equations and Applications, 10 (11). pp. 949-953. ISSN 1023-6198

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Abstract

In this paper we present a new closed-form solution to a chaotic difference equation, $y_{n+1} = a_2 y_{n}^2 + a_1 y_{n} + a_0$ with coefficient $a_0 = (a_1 - 4)(a_1 + 2) / (4 a_2)$, and using this solution, show how corresponding exact roots to a special set of related polynomials of order $2^p, p \in \mathbb{N}$ with two independent parameters can be generated, for any $p$.

Item Type:Article
Subjects:D - G > Dynamical systems and ergodic theory
D - G > Difference and functional equations
H - N > Numerical analysis
Research Groups:Oxford Centre for Industrial and Applied Mathematics
ID Code:176
Deposited By:Max Little
Deposited On:16 May 2005
Last Modified:20 Jul 2009 14:19

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