抛物型Möbius差分方程的Hyers-Ulam稳定性
Hyers-Ulam stability of parabolic Möbius difference equation
摘要：
若黎曼球面上具有复系数的线性分式映射$ ad-bc = 1 $为且为$ a+d = \pm 2 $，则称$ g $为{ \em抛物}莫比乌斯映射.设$ \{ b_n \}_{n \in \mathbb{N}_0} $是抛物型莫比乌斯差分方程$ b_{n+1} = g(b_n) $对每个$ n \in \mathbb{N}_0 $的解。我们证明了序列$ \{ b_n \}_{n \in \mathbb{N}_0} $不具有Hyers-Ulam稳定性。
英文摘要：
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} Möbius map. Let $ \{ b_n \}_{n \in \mathbb{N}_0} $ be the solution of the parabolic Möbius difference equation $ b_{n+1} = g(b_n) $ for every $ n \in \mathbb{N}_0 $. We show that the sequence $ \{ b_n \}_{n \in \mathbb{N}_0} $ has no Hyers-Ulam stability.
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