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We find an optimal quasi-gap condition for a weakly expanding dynamical system associated with Dini potential. Under this optimal quasi-gap condition, we prove the Ruelle operator theorem and further the decay of the correlations for any weakly expanding dynamical systems with Dini potentials.


This is the accepted manuscript of an article published as: Jiang, Yunping and Yuan-Ling Ye, "Decay of correlations for weakly expanding dynamical systems with Dini potentials under optimal quasi-gap condition." Nonlinearity, vol. 35, p. 916, 2021.



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