Statistical properties of physical-like measuresSG is supported by NSFC 11831001 and NSFC 11771025. JY is partially supported by CNPq, FAPERJ, and PRONEX of Brazil and NSFC 11871487 of China.,Nonlinearity

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Statistical properties of physical-like measuresSG is supported by NSFC 11831001 and NSFC 11771025. JY is partially supported by CNPq, FAPERJ, and PRONEX of Brazil and NSFC 11871487 of China.
Nonlinearity ( IF 1.6 ) Pub Date : 2021-02-23 , DOI: 10.1088/1361-6544/abd7c9
Shaobo Gan ₁ , Fan Yang ₂ , Jiagang Yang ₃ , Rusong Zheng ₄

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In this paper we consider the semi-continuity of the physical-like measures for diffeomorphisms with dominated splittings. We prove that any weak-* limit of physical-like measures along a sequence of C ¹ diffeomorphisms {f _n} must be a Gibbs F-state for the limiting map f. As a consequence, we establish the statistical stability for the C ¹ perturbation of the time-one map of three-dimensional Lorenz attractors, and the continuity of the physical measure for the diffeomorphisms constructed by Bonatti and Viana.

更新日期：2021-02-23

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