Asymptotic expansions for the escape rate of stochastically perturbed unimodal maps

The escape rate of a stochastic dynamical system can be found as an expansion in powers of the noise strength. In the 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 αα, the “noise dimension”, remains to be interpreted. This report presents new data for αα showing that the relation to the dimensions is more complicated than predicted in the earlier work and oscillates as a function of the map parameter, in contrast to other dimension-like quantities.