Does there exist a rational function $f\in\Bbb{C}(z)$ whose Julia set coincides with $ \left\{\left(x,\sin\left(\frac{1}{x}\right)\right)\,\Big|\,x\in\left(0,\frac{1}{\pi}\right]\right\}\cup(\{0\}\times[-1,1]) $?
Can the topologist's sine curve be realized as a Julia set?
KhashF
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