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For a summable variation potential function on a subshift of finite type, Pollicott (2000 Trans. Am. Math. Soc. 352 843–53) gave an estimate of the decay of correlations. It was known that the systems he considered have the bounded distortion property (BDP), and that is a key condition on the systems. In this paper, we study weakly expansive Dini dynamical systems that may not have the BDP. Under some assumptions, our theorem gives an estimate of the decay of correlations.
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