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Results tagged with fractional-iteration
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user 2508
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.
32
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0
answers
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$f\circ f=g$ revisited
This may be related to solving $f(f(x))=g(x)$. Let
$C(\mathbb{R})$ be the linear space of all continuous functions from
$\mathbb{R}$ to $\mathbb{R}$, and let $\mathcal{S}:=\{g\in C(\mathbb{R}) ; \exis …
- 4,060
21
votes
solving $f(f(x))=g(x)$
Q2) has a negative answer. Namely, if, e.g., $g(x)=-x$ for all $x\in\mathbb{R}$,
then there is no
continuous
$f:\mathbb{R\rightarrow\mathbb{R}}$ such
that $f\circ f=g$.
As to Q3, see, e.g., Theor …
- 4,060