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Title: Quasi-invariant measures, escape rates and the effect of the hole
Authors: Bahsoun, Wael
Bose, Christopher
Issue Date: 2010
Publisher: © American Institute of Mathematical Sciences
Citation: BAHSOUN, W. and BOSE, C., 2010. Quasi-invariant measures, escape rates and the effect of the hole. Discrete and Continuous Dynamical Systems. Series A, 27 (3), pp.1107-1121.
Abstract: Let T be a piecewise expanding interval map and T H be an abstract perturbation of T into an interval map with a hole. Given a number l, 0 < l < 1, we compute an upper-bound on the size of a hole needed for the existence of an absolutely continuous conditionally invariant measure (accim) with escape rate not greater than-In(1-l). The two main ingredients of our approach are Ulam's method and an abstract perturbation result of Keller and Liverani.
Description: This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Discrete and Continuous Dynamical Systems, Series A following peer review. The definitive publisher-authenticated version, BAHSOUN, W. and BOSE, C., 2010. Quasi-invariant measures, escape rates and the effect of the hole. Discrete and Continuous Dynamical Systems. Series A, 27 (3), pp.1107-1121, is available online at: https://doi.org/10.3934/dcds.2010.27.1107.
Sponsor: W.B. thanks the Department of Mathematics and Statistics at the University of Victoria, Canada, for hosting him during May-June 2009. His visit was supported by by Loughborough University Small Faculty Grant number H10621.
Version: Accepted for publication
DOI: 10.3934/dcds.2010.27.1107
URI: https://dspace.lboro.ac.uk/2134/26317
Publisher Link: https://doi.org/10.3934/dcds.2010.27.1107
ISSN: 1078-0947
Appears in Collections:Published Articles (Maths)

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