Analytic Solutions of a Functional Equation for Invariant Curves1

An iterative functional equation is deduced by C. T. Ng and W. Zhang Ž1997, 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