Consider the function $g(x) = -3x^2/2 - x/2 + 1$. When iterated it has a 3 cycle, so therefore, according to Sharkovskii's theorem, it has cycles of all integer lengths (as well as chaotic infinite ones). Is it possible to define a (certainly multivalued) function f(x) that returns a number between -2 and +2 that is one of the destinations along the cycle? Say f(17) would return one of the numbers in the 17 cycle?
2026-04-06 11:01:13.1775473273
Naïve question about functions with a 3 cycle
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