Hyers-Ulam stability of elliptic Möbius difference equation

Abstract: The linear fractional map $ f(z) = \frac{az+ b}{cz + d} $ on the Riemann sphere with complex coefficients $ ad-bc \neq 0 $ is called M\"obius map. If $ f $ satisfies $ ad-bc=1 $ and $ -2<a+d<2 $, then $ f $ is called $\textit{elliptic}$ 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.