This shows \( \mathrm{tet}(f(e^{it})) \) for your mapping (base-\( e \) tetration), with \( t \) going from \( -\pi \) to \( \pi \):
There is a small corner in the real part (red curve). This may slow down convergence of a Fourier series. The rescaled mapping has a much nastier spike, however, and so doesn't seem very useful
There is a small corner in the real part (red curve). This may slow down convergence of a Fourier series. The rescaled mapping has a much nastier spike, however, and so doesn't seem very useful