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Results tagged with fractional-iteration
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user 3172
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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votes
How to solve $f(f(x)) = \cos(x)$?
Henrik's idea is good, but it doesn't quite work for $\cos x$ since the power series must have a non-zero leading term, and so can't be substituted into a power series. To fix this, consider a power s …
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