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Operator renewal theory for continuous time dynamical systems with finite and infinite measure

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Melbourne, Ian and Terhesiu, Dalia (2017) Operator renewal theory for continuous time dynamical systems with finite and infinite measure. Monatshefte fur Mathematik, 182 (2). pp. 377-431. doi:10.1007/s00605-016-0922-0 ISSN 0026-9255.

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Official URL: http://dx.doi.org/10.1007/s00605-016-0922-0

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Abstract

We develop operator renewal theory for flows and apply this to obtain results on mixing and rates of mixing for a large class of finite and infinite measure semiflows. Examples of systems covered by our results include suspensions over parabolic rational maps of the complex plane, and nonuniformly expanding semiflows with indifferent periodic orbits. In the finite measure case, the emphasis is on obtaining sharp rates of decorrelations, extending results of Gouëzel and Sarig from the discrete time setting to continuous time. In the infinite measure case, the primary question is to prove results on mixing itself, extending our results in the discrete time setting. In some cases, we obtain also higher order asymptotics and rates of mixing.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH): Ergodic theory
Journal or Publication Title: Monatshefte fur Mathematik
Publisher: Springer Vienna
ISSN: 0026-9255
Official Date: February 2017
Dates:
DateEvent
February 2017Published
25 May 2015Available
9 May 2015Accepted
Volume: 182
Number: 2
Number of Pages: 50
Page Range: pp. 377-431
DOI: 10.1007/s00605-016-0922-0
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Date of first compliant deposit: 7 June 2016
Date of first compliant Open Access: 25 May 2017
Funder: Engineering and Physical Sciences Research Council (EPSRC), European Research Council (ERC)
Grant number: EP/F031807/1 (EPSRC), 320977 (ERC), 246953 (ERC)

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