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Fluctuations of ergodic sums on periodic orbits under specification

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  • 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.

    Mathematics Subject Classification: Primary: 37A50; Secondary: 37B99, 60F05.

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