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

The linear fractional map $g(z)=\frac{az+b}{cz+d}$ on the Riemann sphere with complex coefficients $ad-bc=1$ is and $a+d=\pm 2$, then $g$ is called {\em parabolic} M"obius map. Let $\{b_n{\}}_{n\in {\mathbb{N}}_0}$ be the solution of the parabolic M"obius difference equation $ b_{n+1} = g(b_n) $forevery$ n \in $\mathbb{N}$0 $\mathrm{.}Weshowthatthesequence$ { b_n }{n \in $\mathbb{N}$_0} $ has no Hyers-Ulam stability.