Resumen de Möbius splines are closed under continuous iteration

R. J. Martin

• The continuous or fractional iterates of a piecewise Möbius (linear / linear) function, or Möbius spline, are also piecewise Möbius. Further, they may be calculated exactly via a simple algorithm. The same remarks apply to the related Schröder equation. Some numerical demonstrations are given. It is suggested that this technique could be used to approximate continuous iterates of an arbitrary function, with possible applications in statistics, signal processing and computer graphics. We also suggest that Möbius splines are a useful tool in the numerical solution of more general functional equations.