Hyers-Ulam stability of elliptic M\"obius difference equation

The linear fractional map $f(z)=\frac{az+b}{cz+d}$ on the Riemann sphere with complex coefficients $ad-bc\mathrm{\ne }0$ is called M"obius map. If $f$ satisfies $ad-bc=1$ and $-2<a+d<2$, then $f$ is called $\mathit{\text{elliptic}}$ M"obius map. Let $\{b_n{\}}_{n\in {\mathbb{N}}_0}$ be the solution of the elliptic M"obius difference equation $b_{n+1}=f(b_n)$ for every $n\in {\mathbb{N}}_0$. Then the sequence $ { b_n }_{n \in $\mathbb{N}$_0} $ has no Hyers-Ulam stability.