In this talk, we will report some recent progress of the study on chaotic behavior of hyperbolic dynamical systems, which mainly contains two parts: (1)Existence of periodic orbits and Smale horseshoes; (2) Ergodic optimization theory. This is based on the joint works with Wen Huang, Kening Lu, Xiao Ma, Leiye Xu, Lai-sang Young, and Yiwei Zhang.
连增，四川大学数学学院教授，博士生导师，国家杰出青年科学基金获得者，教育部长江学者奖励计划特聘教授。研究领域为：随机动力系统与遍历理论。在J. Amer. Math. Soc.，Mem. Amer. Math. Soc.等国际顶级期刊发表学术论文多篇。
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