# Questions tagged [fractional-iteration]

The study of fractional self-iterations of a map. A basic example is the analysis of functional square roots of a map $g$, i.e. solutions $f$ to the functional equation $f \circ f = g$. The continuous version of fractional iteration concerns maps which have flows. This case is also known as continuous iteration. A classic example is the problem of extending tetration to the real and complex numbers.

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### $f\circ f=g$ revisited

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### elementary Abel function of a polynomial

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### Generalization of Carleman coefficients to multivariable functions - Carleman tensor?

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### Fractional iteration of a variant of the $\sin()$ function - how to fractionally iterate $ f(x)=\sum_{k=1}^\infty (-1)^k a_{2k}x^{2k}$?

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### Fractional exponentiation with different bases

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### Analytic Tetration and Natural Rates of Growth

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