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Results tagged with complex-dynamics
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user 39521
Dynamics of holomorphic transformations; Mandelbrot and Julia sets.
13
votes
Accepted
Exponential towers of $i$'s
Let $f : \mathcal{P}(\mathbb{C}) \rightarrow \mathcal{P}(\mathbb{C})$ be the function on the powerset of the complex numbers defined by:
$$ f(A) = \left\{ \exp\left( \frac{\pi i}{2}(4n + 1)z \right) …
- 12.4k
3
votes
Accepted
What about the other $f$ such that $f(f(x)) = \sin(x)$?
Clearly, if $f_+(z)$ is a functional square-root of $\sin(z)$, then so is $g(z) := -f_+(-z)$; moreover, they have the same derivative at the origin. Hence, your post implies that $g(z) = f_+(z)$, so $ …
- 12.4k