If there is a $\delta$ error, will the orbit converge to given orbit?
$F(x+\delta) = F(x)+F’(x)\delta + \mathcal{O}(\delta^2)$
Hence, $\delta F^n = (F’)^n$
Hence, if $||F’(x^*)||<1$, we have stability.
For stability of p Orbit, we find the stability of fixed points of $F^p$
$|\lambda_p|=\begin{cases}
>1& \implies \text{unstable}
<1& \implies \text{stable}
=0& \implies \text{super stable}
\end{cases}$
For the [2022-01-07#Tent Map|Tent Map], all orbits are unstable as $F’ = 2$ always.