Möbius splines are closed under continuous iteration (Q1861182)

The paper is devoted to explicit computational procedures for exactly computing the fractional iterates of a Möbius spline, i.e. a function that is monotonic, continuously differentiable and is piecewise homographic transformation. It is shown that the fractional iterate of a Möbius spline is itself a Möbius spline. A simple algorithm for computing composition and fractional iterates is suggested. There is some discussion of applying Möbius splines in numerical solution of functional equations.