Stable Sets and Chaos in Positive Entropy Systems

报告题目: Stable Sets and Chaos in Positive Entropy Systems

报告人:  黄文 教授

报告时间: 1119日(周六)    下午14:00

报告地点: 狮子山校区6教811


报告摘要:

In this talk, I will present the chaotic phenomenon of a dynamical system with positive entropy. It is shown that a dynamical system has positive entropy if and only if it has a weak horseshoe. Particularly, I will show that a Lorentz attractor has a weak horseshoe. Moreover, I will present the Hausdorff dimension and the chaotic behavior of stable sets and unstable sets in a C1-diffeomorphism system with positive entropy. The lower bound of the Hausdorff dimension of these stable sets and unstable sets is given in terms of the metric entropy and the largest Lyapunov exponent.


专家介绍:

黄文,中国科学技术大学教授,国家杰出青年基金获得者,从事遍历理论与拓扑动力系统研究,近年来在熵理论及其与数论相关的问题方面取得进展,相关结果接受发表在CPAM, MAMS, ADV.MATH.等数学杂志上.