zero's of exp^[1/2](x) ?

[mike3]

Hmm. What's so "fascinating" about the "mild singularity", anyway? I'd expect that precisely because \( \exp^{1/2} \) is an iterate of \( \exp \), that it would have fixed points wherever \( \exp \) does, on the appropriate branch of course (note how \( \log \) has the same fixed points as \( \exp \), with different branches giving different fixed points.). On this branch, \( L \) and \( \bar{L} \) are fixed.

Not sure how I could prepare a graph with the branch cut reoriented, however, because new branch points start to appear and I'm not at all sure how to handle all that cutting since there doesn't seem any easy way to "anticipate" what points will be branch points, anyway.