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Dynamics of holomorphic transformations; Mandelbrot and Julia sets.

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When does iterating $z \mapsto z^2 + c$ have an exact solution?

If one iterates the map $z \mapsto z^2 + c$ there is obviously a simple formula for the sequence one gets if $c=0$. Less obviously, there is also a simple formula when $c = -2$ (use the identity $2 \c …
Richard Borcherds's user avatar