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Approximating the maximum ergodic average via periodic orbits
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Collier, D. and Morris, Ian D. (2008) Approximating the maximum ergodic average via periodic orbits. Ergodic Theory and Dynamical Systems, Vol.28 (No.4). pp. 1081-1090. doi:10.1017/S014338570700082X ISSN 0143-3857.
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Official URL: http://dx.doi.org/10.1017/S014338570700082X
Abstract
Let sigma: Sigma(A) -> Sigma(A) be a subshift of finite type, let M-sigma be the set of all sigma-invariant Borel probability measures on Sigma(A), and let f : Sigma(A) -> R be a Holder continuous observable. There exists at least one or-invariant measure A which maximizes integral f d mu. The following question was asked by B. R. Hunt, E. Ott and G. Yuan: how quickly can the maximum of the integrals integral f d mu be approximated by averages along periodic orbits of period less than p? We give an example of a Holder observable f for which this rate of approximation is slower than stretched-exponential in p.
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, Combinatorial dynamics, Mathematical optimization | ||||
Journal or Publication Title: | Ergodic Theory and Dynamical Systems | ||||
Publisher: | Cambridge University Press | ||||
ISSN: | 0143-3857 | ||||
Official Date: | August 2008 | ||||
Dates: |
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Volume: | Vol.28 | ||||
Number: | No.4 | ||||
Page Range: | pp. 1081-1090 | ||||
DOI: | 10.1017/S014338570700082X | ||||
Status: | Peer Reviewed | ||||
Access rights to Published version: | Open Access (Creative Commons) |
Data sourced from Thomson Reuters' Web of Knowledge
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