Measures of maximal entropy can characterize the global stability of a system from a measure-theoretic perspective. There is considerable interest in investigating the existence, finiteness, and deep ergodic properties of maximal entropy measures. For non-uniformly hyperbolic diffeomorphisms, advances in this direction have been made by Newhouse, Buzzi, Crovisier, Sarig, and others. In this talk, we present recent progress on measures of maximal entropy for three-dimensional vector fields with singularities. For instance, we manage to prove the finiteness of measures of maximal entropy for three-dimensional $C^\infty$ vector fields with positive topological entropy.This is a joint work with J. Buzzi, S. Crovisier, Y. Lima and C. Luo.
杨大伟，苏州大学教授，博士生导师，国家级高层次领军人才，长期从事微分动力系统及其遍历理论的研究，特别是在Palis稠密性猜测、SRB测度、有奇点向量场的动力学、熵理论等方面取得了一系列进展，并在Ann. Sci. Éc. Norm. Super.、J. Eur. Math. Soc.、Adv. Math.、Comm. Math. Phys.、Trans. Amer. Math. Soc.、Math. Z.、Sci. China Math.等期刊发表了多篇学术论文；主持多项国家自然科学基金面上项目，参与国家自然科学基金委重大项目、科技部重点专项等项目；获得教育部自然科学一等奖（第二参与人）、江苏省自然科学三等奖（第三参与人）、江苏省特聘教授、江苏省数学成就奖、姑苏领军人才等多项荣誉。
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