The logistic map $x_{n+1} = r(x_{n}(1-x_{n+1}))$ has clopsed form solutions for $r=2$, $r=4$, and $r=-2$. It is conjectured that these are the only values of $r$ for which closed form solutions exist. How can one solve this difference equation for these three values of $r$?
2026-04-18 23:03:17.1776553397
closed form solutions for the logistic map
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