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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
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 | ||||||||
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| 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: |
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| 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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