Semi-horseshoes,
invariant tori and entropy
in partially hyperbolic systems
报告专家：马啸 副教授 （中国科学技术大学）
报告时间：7月29日（周二） 下午15:00--15:50
报告地点：国家天元数学西南中心516
报告摘要：
In this talk, we consider the growth rate of numbers of invariant tori and horseshoe-like structure in partially hyperbolic systems.
1) For a class of affine Anosov mappsings with a quasi-periodic forcing, there is a unique positive integer $m$, which only depends on the system, such that the exponential growth rate of the number of invariant tori of degree $m$ is equal to the topological entropy.
2) For $C^1$ partially hyperbolic systems with multiple expanding directions, saying $E_1,\ldots, E_{s}$, we show the topological entropy of the semi-horseshoe is bounded from below by $\sum_{s'=1}^s\dim E_{s'}\log\lambda_{s'}$, where $\lambda_{s'}$ is the expanding rate of $E_{s'}$.
This talk is based on joint works with Xinyu Bai, Wen Huang, Zeng Lian, Xue Liu, Leiye Xu and Hang Zhao.
邀请人：史逸
