Average exit times in volume preserving maps

Abstract

For a volume preserving map, the exit time, averaged over the incoming set of a region, is given by the ratio of the measure of the accessible subset of the region to that of the incoming set. This result is primarily of interest to show two things: first it gives a simple bound on the algebraic decay exponent of the survival probability. Second, it gives a tool which permits the computation of the measure of the accessible set. We use this to find the measure of the bounded orbits for H\'enon's quadratic map.