Bifurcation of Almost Periodic Solutions in a Difference Equation

Abstract This paper is concerned with almost periodic solutions (in short, ap-solutions) originating from an equilibrium state when the parameters of a difference equation are varied. We study the bifurcation of ap-solutions for an ap-difference equation of the form xn+1 = f(n, xn;µ), using the Green’s function for regular ap-operators and Σ-operators.