LOCAL ESCAPE RATE DICHOTOMY FROM A PROBABILITY POINT OF VIEW

Abstract

We will discuss a dichotomy pertaining to escape rates in dynamical systems. This dichotomy pertains to the limiting behavior of the escape rate as it is compared to the size of a shrinking hole (the local escape rate). In this case, it has been shown, with some robustness, that under certain mixing conditions on the system this limiting behavior is determined by the periodicity of of the set to which the hole shrinks. We will use a blocking argument to obtain error estimates for truncation of the limit described above. These will allow for the result that the double limit describing the local escape rate to be taken along different paths. Finally, we will discuss a result that ties the escape rate conditioned on being in the hole, to the usual escape rate.