The linear fractional map f (z) = az+b cz+d on the Riemann sphere with complex coefficients ad − bc = 0 is called Möbius map. If f satisfies ad − bc = 1 and −2 < a + d < 2, then f is called elliptic Möbius map. Let {b n } n∈N 0 be the solution of the elliptic Möbius difference equation b n+1 = f (b n ) for every n ∈ N 0 . Then the sequence {b n } n∈N 0 has no Hyers-Ulam stability.
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