  Recent advances in the periodic orbit theory of stochastically perturbed
systems have permitted a calculation of the escape rate of a noisy chaotic map
to order 64 in the noise strength. Comparison with the usual asymptotic
expansions obtained from integrals and with a previous calculation of the
electrostatic potential of exactly selfsimilar fractal charge distributions,
suggests a remarkably accurate form for the late terms in the expansion, with
parameters determined independently from the fractal repeller and the critical
point of the map. Two methods give a precise meaning to the asymptotic
expansion, Borel summation and Shafer approximants. These can then be compared
with the escape rate as computed by alternative methods.
