I have the following discrete map: \begin{equation} x_{n+1}=μ-x^4 \end{equation} for which I have used manipulate to see the way the system evolves depending on the real parameter $μ$:
Manipulate[
ListLinePlot[
NestList[μ - #^4 &, x0, 100],
PlotRange -> {0, 1},
ImageSize -> {450, 375}],
{{μ, 0.8, "parameter μ"}, 0, 4, Appearance -> "Labeled"},
{{x0, 0.2, "Initial \!\(\*SubscriptBox[\(x\), \(0\)]\)"},
0, 1, Appearance -> "Labeled"}]
What I would like to do is to show in some way the coordinates on the plot, so that one can see the values of $x$ for which a cycle 2 is defined, a cycle 4 is defined, a cycle 8 and so on. If that is not possible, how could I for example print below the plot, the last 16 coordinates of the 100th iteration in this particular map? (so that one can see the recurrence of the 2,4,8,... points).
Thanks!