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arXiv · 1805.01973

Fluctuations of ergodic sums on periodic orbits under specification

Manfred Denker·Samuel Senti·Xuan Zhang
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Abstract

We study the fluctuations of ergodic sums using global and local specifications on periodic points. We obtain Lindeberg-type central limit theorems in both situations. As an application, when the system possesses a unique measure of maximal entropy, we show weak convergence of ergodic sums to a mixture of normal distributions. Our results suggest decomposing the variances of ergodic sums according to global and local sources.

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Manfred Denker, Samuel Senti, Xuan Zhang. 2018-05-05. Fluctuations of ergodic sums on periodic orbits under specification. https://doi.org/10.3934/dcds.2020197

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