Fractal approximants on the circle

A methodology based on fractal interpolation functions is used in this work to define new real maps on the circle generalizing the classical ones. The power of fractal methodology allows us to generalize any other interpolant, both smooth and non-smooth, but the important fact is that this technique provides one of the few methods of non-differentiable interpolation. In this way, it constitutes a func- tional model for chaotic processes. In this article we study a generalization of some approximation formulae proposed by Dunham Jackson both in classical and fractal cases.