Hyers-Ulam stability of loxodromic Möbius difference equation

2018/08/28 by Nam, Young Woo
#39A30 #39A45 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1808.09813

Abstract

Hyers-Ulam of the sequence \z_n\_{n ∈ ℕ} satisfying the difference equation z_i+1 = g(z_i) where g(z) = (az + b)/(cz + 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 \z_n\_{n ∈ ℕ} is in the exterior of avoided region, which is the union of the certain disks of g^-n(∞) for all n ∈ ℕ .

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