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Period-3 Orbits via Sylvester`s Theorem and Resultants

by Jaqueline Burm and Paul Fishback

This article originally appeared in:
Mathematics Magazine
February, 2001

Subject classification(s): Differential & Difference Equations | Dynamical Systems | Chaos
Applicable Course(s): 3.6 Differential Equations | 4.15 Advanced Differential Equations

The authors study period-\(3\) orbits of the logistic function \( f_r(x)=rx(1-x)\), and provide another derivation of the fact that \(r_0=1+\sqrt {8}\), where \( r_0\) is the smallest positive value of \(r\) for which \(f_r^3(x)=x\) has a solution \(x_0\) which is not a fixed point of \(f_r\).

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