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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. 10811090. ISSN 01433857

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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 Msigma be the set of all sigmainvariant Borel probability measures on Sigma(A), and let f : Sigma(A) > R be a Holder continuous observable. There exists at least one orinvariant 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 stretchedexponential in p.
Item Type:  Journal Article 

Subjects:  Q Science > QA Mathematics 
Divisions:  Faculty of 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:  01433857 
Official Date:  August 2008 
Volume:  Vol.28 
Number:  No.4 
Page Range:  pp. 10811090 
Identification Number:  10.1017/S014338570700082X 
Status:  Peer Reviewed 
Access rights to Published version:  Open Access 
References:  [1] Brémont, J.. Gibbs measures at temperature zero. Nonlinearity 16 (2003), 419–426. 
URI:  http://wrap.warwick.ac.uk/id/eprint/864 
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