The Different Fixed Points of Exponentials
#4
I apologize for my fractal "n00bness"... but is there available a diagram of the complex plane showing in addition to the fixed points also the shapes and positions of their respective basin of attraction? I'm interested in visualizing the sets \(A_p=\{z\in\mathbb C\, :\, \lim_{n\to \infty} \exp_b ^n(z)=p\}\).

What is the knowledge about the set \(A=\bigcup_{p\in {\rm fix}(\exp_b)}A_p\) and the set \(\mathbb C\setminus A\). Are they open? Closed? Connected by arcs? Are they punctured/have holes?

Mother Law \(\sigma^+\circ 0=\sigma \circ \sigma^+ \)

\({\rm Grp}_{\rm pt} ({\rm RK}J,G)\cong \mathbb N{\rm Set}_{\rm pt} (J, \Sigma^G)\)
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RE: The Different Fixed Points of Exponentials - by MphLee - 07/07/2022, 08:29 PM

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