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Approximating the maximum ergodic average via periodic orbits
Published online by Cambridge University Press: 01 August 2008
Abstract
Let σ:ΣA→ΣA be a subshift of finite type, let be the set of all σ-invariant Borel probability measures on ΣA, and let be a Hölder continuous observable. There exists at least one σ-invariant measure μ which maximizes . The following question was asked by B. R. Hunt, E. Ott and G. Yuan: how quickly can the maximum of the integrals be approximated by averages along periodic orbits of period less than p? We give an example of a Hölder observable f for which this rate of approximation is slower than stretched-exponential in p.
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- Copyright © 2008 Cambridge University Press
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