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In this paper escape rates and local escape rates for special flows aresudied. In a general context the first result is that the escape rate dependsmonotonically on the ceiling function and fulfills certain scaling, invariance,and continuity properties. For the metric setting local escape rates areconsidered. If the base transformation is ergodic and exhibits an exponentialconvergence in probability of ergodic sums, then the local escape rate withrespect to the flow is just the local escape rate with respect to the basetransformation, divided by the integral of the ceiling function. Also areformulation with respect to induced pressure is presented. Finally, underadditional regularity conditions higher order asymptotics for the local escaperate are established.

Escape rates for special flows and their higher order asymptotics