报告时间：2026年4月14日（周二）上午 09:30-10:30
报告地点：苏州大学纯水楼303
报告人：罗炽逸，江西师范大学
报告摘要：
The upper semi-continuity continuity of the entropy map has attracted significant interest, as it ensures the existence of measures of maximal entropy. We prove that for C^{1+} three-dimensional diffeomorphisms, the entropy function is upper semi-continuous under a simple condition: if an invariant measure is a continuity point of the sum of positive Lyapunov exponents, then it is an upper-semi continuity point of the metric entropy. We also prove that, for dominated splitting systems in arbitrary dimensions, the entropy map is upper semi-continuous under a sign-separated condition on the Lyapunov exponents.
This result not only provides a converse perspective to the work of Buzzi-Crovisier-Sarig (Invent. Math., 2022), which showed that entropy continuity implies Lyapunov exponent continuity for C^∞ surface diffeomorphisms but also improve some result in Buzzi-Crovisier-Sarig's paper on SPR property for surface diffeomorphisms.
邀请人：杨大伟