Approximating the maximum ergodic average via periodic orbits
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. ISSN 0143-3857
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Official URL: http://dx.doi.org/10.1017/S014338570700082X
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 > 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|
|Official Date:||August 2008|
|Page Range:||pp. 1081-1090|
|Access rights to Published version:||Open Access|
 Brémont, J.. Gibbs measures at temperature zero. Nonlinearity 16 (2003), 419–426.
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