波莱-雷尼图上说明的遍历量的有效估计值

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED Nonlinearity Pub Date : 2024-07-24 DOI:10.1088/1361-6544/ad6053

Mark Pollicott and Julia Slipantschuk

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引用次数: 0

摘要

我们提出了一种实用有效的方法，可以非常精确地严格估计与转移算子顶特征值相关的量。该方法结合了拉格朗日-切比雪夫近似的显式误差约束和成熟的最小最大法。我们通过显著提高对与博尔耶-雷尼图谱相关的各种遍历量的严格估计来说明该方法的适用性。

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Effective estimates of ergodic quantities illustrated on the Bolyai-Rényi map

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.

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来源期刊

Nonlinearity 物理-物理：数学物理

CiteScore

3.00

自引率

5.90%

发文量

170

审稿时长

12 months

期刊介绍： Aimed primarily at mathematicians and physicists interested in research on nonlinear phenomena, the journal''s coverage ranges from proofs of important theorems to papers presenting ideas, conjectures and numerical or physical experiments of significant physical and mathematical interest. Subject coverage: The journal publishes papers on nonlinear mathematics, mathematical physics, experimental physics, theoretical physics and other areas in the sciences where nonlinear phenomena are of fundamental importance. A more detailed indication is given by the subject interests of the Editorial Board members, which are listed in every issue of the journal. Due to the broad scope of Nonlinearity, and in order to make all papers published in the journal accessible to its wide readership, authors are required to provide sufficient introductory material in their paper. This material should contain enough detail and background information to place their research into context and to make it understandable to scientists working on nonlinear phenomena. Nonlinearity is a journal of the Institute of Physics and the London Mathematical Society.

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