(11/16/2009, 08:08 PM)mike3 Wrote: So perhaps \( b = e^{1/e} \) isn't a singularity after all, though there are other points on the boundary that are, which would agree with the results from the Taylor experiment.
Unfortunately from the picture you can not conclude that it is no singularity. Isolated singularities have this behaviour to take on nearly every value in each neighborhood, branchpoints however can be quite wellbehaved, e.g. the pictures for sqrt are:
My guess is that the "proper" singularities (i.e. those with chaotic behaviour taking nearly every point in each neighborhood) are dense on the TSR boundary. So that no continuable path leads outside the TSR.
