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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

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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
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:
DateEvent
August 2008Published
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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