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 α , the “noise dimension”, remains to be interpreted. This report presents new data for α 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.