2017/08/29 by Nam, Young Woo
#39A45 #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1708.08662
Hyers-Ulam stability of the difference equation with the initial point z0 as follows zi+1 = (azi + b)/(czi + d) is investigated for complex numbers a,b,c and d where ad - bc = 1 , c ≠ 0 and a + d ∈ ℝ ∖ [-2,2] . The stability of the sequence \zn\n ∈ ℕ0 holds if the initial point is in the exterior of a certain disk of which center is -(d)/(c) . Furthermore, the region for stability can be extended to the complement of some neighborhood of the line segment between -(d)/(c) and the repelling fixed point of the map z ↦ (az + b)/(cz + d) . This result is the generalization of Hyers-Ulam stability of Pielou logistic equation.