Hyers–Ulam stability of loxodromic Möbius difference equation

摘要

Hyers–Ulam stability of the sequence {zn}n∈N satisfying the difference equation zn+1=g(zn) where g(z)=az+bcz+d with complex numbers a, b, c and d is defined. Let g be loxodromic Möbius map, that is, g satisfies that ad−bc=1 and a+d∈C∖[−2,2]. Hyers–Ulam stability holds if the initial point of {zn}n∈N is in the exterior of avoided region, which is the union of the certain disks of g−n(∞) for all n∈N.