Analytic Solutions of a Functional Equation for Invariant Curves

Abstract An iterative functional equation is deduced by C. T. Ng and W. Zhang (1997, J. Differ. Equations Appl. 3 , 147–168) from the problem of invariant curves. In this paper, its analytic solutions are discussed by locally reducing the equation to another functional equation without iteration and by constructing solutions in uniformly convergent power series for the latter equation.