Can the recursion $x_{n+1} = 3{(x_n)}^2+2$ with $x_0 = 2$, be solved?

Asked Feb 05 '17 at 00:12

Active Feb 05 '17 at 07:45

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This can be solved computationally, but is there an analytical solution? I've tried to build a solution and it wasn't pretty. $$x_{n+1} = 3{(x_n)}^2+2 \qquad x_0 = 2$$

edited Feb 05 '17 at 07:45

Did

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asked Feb 05 '17 at 00:12

Aspiring Mathematician

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The recursion $$z\mapsto z^2+c$$ is well known to have no analytical solution in general (some entire books with nice images have been written on the subject). – Did Feb 05 '17 at 07:43

Can the recursion $x_{n+1} = 3{(x_n)}^2+2$ with $x_0 = 2$, be solved?

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