  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.
