Über Ausströmraten spezieller Flüsse

Abstract

This thesis examines escape rates for suspension flows with a hole, focusing on the relation between the escape rate and the ceiling function. It is shown that the escape rate depends continuously on the ceiling function with regard to the supremum norm, that the reciprocal of the escape rate is sublinear if the base transformation of the flow is a Markov shift and that the escape rate can be expressed as an induced pressure. For the local escape rate it is shown that under suitable conditions its value depends on the ceiling function only through its integral. Furthermore, the behaviour of the escape rate is investigated for holes shrinking towards a periodic point. For flows that arise from a cylinder function over a Markov shift, one obtains a kind of power series expansion for the escape rate. It is shown that it is sufficient to know the escape rates with respect to the flow and the measure of sets in the basis in order to recover the orbit lengths of periodic points of the flow.