  The escape rate of a stochastic dynamical system can be found as an expansion
in powers of the noise strength. In previous work the coefficients of such an
expansion for a one-dimensional map were fitted to a general form containing a
few parameters. These parameters were found to be related to the fractal
structure of the repeller of the system. The parameter alpha, the "noise
dimension", remains to be interpreted. This report presents new data for alpha
showing that the relation to the dimensions is more complicated than predicted
in earlier work and oscillates as a function of the map parameter, in contrast
to other dimension-like quantities.
