We have linked together two contributions in the development of configurational thermostats, the BT thermostat and the SDC scheme. We have shown that recently proposed configurational thermostats are generalized and enriched in both understanding and
content by the SDC scheme. We have presented the stochastic counterpart to the configurational thermostat.
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.
