# Period-3 Orbits via Sylvester`s Theorem and Resultants

by Jaqueline Burm and Paul Fishback

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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