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Results tagged with fractional-iteration
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user 156054
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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Does the exponential function have a (compositional) square root?
Assume that this half-exponential function $h(x)$ is of the form $a+bx+cx^2$, or a quadratic function. Attempting to expand out $h(h(x))$ gives us the following:
$$h(h(x)) = a+ab+b^{2}x+bcx^{2}+a^{2} …
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