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Escape rates for special flows and their higher order asymptotics

Published online by Cambridge University Press:  25 September 2017

FABIAN DREHER  and
MARC KESSEBÖHMER
FABIAN DREHER
Affiliation:
Fachbereich 3 – Mathematik und Informatik, Universität Bremen, Bibliothekstraße 1, 28359 Bremen, Germany email fdreher@uni-bremen.de, mhk@math.uni-bremen.de
MARC KESSEBÖHMER
Affiliation:
Fachbereich 3 – Mathematik und Informatik, Universität Bremen, Bibliothekstraße 1, 28359 Bremen, Germany email fdreher@uni-bremen.de, mhk@math.uni-bremen.de
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Abstract

In this paper escape rates and local escape rates for special flows are studied. In a general context the first result is that the escape rate depends monotonically on the ceiling function and fulfils certain scaling, invariance and continuity properties. In the context of metric spaces local escape rates are considered. If the base transformation is ergodic and exhibits an exponential convergence in probability of ergodic sums, then the local escape rate with respect to the flow is just the local escape rate with respect to the base transformation, divided by the integral of the ceiling function. Also, a reformulation with respect to induced pressure is presented. Finally, under additional regularity conditions higher order asymptotics for the local escape rate are established.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 39 , Issue 6 , June 2019 , pp. 1501 - 1530
Copyright
© Cambridge University Press, 2017 

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