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Chaotic root-finding for a small class of polynomials

By M. A. Little and D. Heesch

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 $p$

Topics: Dynamical systems and ergodic theory, Difference and functional equations, Numerical analysis
Year: 2004
DOI identifier: 10.1080/10236190412331285351
OAI identifier: oai:generic.eprints.org:176/core69

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