天元讲堂(12.2)动力系统系列报告
1. 题 目 : SRB measures for partially hyperbolic systems with multi 1D centers
报告人:糜泽亚(南京信息工程大学)
时间:2018年12月2日下午 1:20-2:00
地点:数学楼二楼报告厅
摘要: We prove the the existence of Sinai-Ruelle-Bowen measures for partially hyperbolic systems with multi 1 D centers. This is motivated by conjectures of Palis on the existence of physical (Sinai-Ruelle-Bowen) measures for global dynamics. This is a joint work with Yongluo Cao and Dawei Yang.
2. 题目:Periodic approximation of Lyapunov exponents for quasi-compact Banach cocycles
报告人:邹瑞(南京信息工程大学)
时间:2018年12月2日下午 2:00-2:40
地点:数学楼二楼报告厅
摘要:We consider cocycles with values in the set of invertible bounded linear operators on a Banach space. We prove that if the base system has enough hyperbolicity, and the cocycles are quasi-compact, then the Lyapunov exponents of ergodic measures can be approximated by the exponents of measures on periodic orbits.
3. 题目:The approximation of Lyapunov exponents by horseshoes for $C^1$ diffeomorphisms with dominated splitting
报告人:王娟(上海工程技术大学)
时间:2018年12月2日下午 2:40-3:20
地点:数学楼二楼报告厅
摘要:Let f be a $C^1$-diffeomorphism and $\mu$ be a hyperbolic ergodic $f$-invariant Borel probability measure with positive measure-theoretic entropy. Assume that the Oseledec splitting
$$T_xM = E_1(x)\oplus\cdots\oplus E_s(x) \oplus E_{s+1}(x)\oplus\cdots\oplus E_l(x)$$
is dominated on the Oseledec basin $\Gamma$. We give extensions of Katok's Horseshoes construction. Moreover there is a dominated splitting corresponding to Oseledec subspace on horseshoes