Effective estimates of ergodic quantities illustrated on the Bolyai-Rényi map
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Published:2024-07-25
Issue:9
Volume:37
Page:095013
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ISSN:0951-7715
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Container-title:Nonlinearity
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language:
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Short-container-title:Nonlinearity
Author:
Pollicott Mark,Slipantschuk Julia
Abstract
Abstract
We present a practical and effective method for rigorously estimating quantities associated to top eigenvalues of transfer operators to very high precision. The method combines explicit error bounds of the Lagrange-Chebyshev approximation with an established min-max method. We illustrate its applicability by significantly improving rigorous estimates on various ergodic quantities associated to the Bolyai–Rényi map.
Funder
H2020 European Research Council
Engineering and Physical Sciences Research Council
Reference28 articles.
1. A rigorous computational approach to linear response;Bahsoun;Nonlinearity,2018
2. Lagrange approximation of transfer operators associated with holomorphic data;Bandtlow,2020
3. Hausdorff dimension of quasi-circles;Bowen;Publ. Math. I.H.E.S.,1979