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Möbius splines are closed under continuous iteration. (English) Zbl 1017.65104
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.

MSC:
65Q05 Numerical methods for functional equations (MSC2000)
39B12 Iteration theory, iterative and composite equations
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