研究生教育创新计划高水平学术前沿讲座之三十二
 

报告人：连增 教授
        Loughborough University, UK

系列之I (2 hrs)

题目: Lyapunov exponents and Multiplicative Ergodic Theorem for Random Dynamical Systems in Separable Banach spaces.
摘要: We study the Lyapunov exponents and corresponding invariant subspaces for random dynamical systems in a separable Banach space, which could be generated by a stochastic PDE, and prove a version of Multiplicative Ergodic Theorem. In this talk, I will report both the result and the framework of the proof. This is a joint work with Kening Lu at BYU.
时间： 4月15日(周一）下午3:30-5:30
地点： 数学科学学院1611教室

系列之II (1 hrs)

题目: Lyapunov exponents, periodic orbits, and horseshoe for semiflows in Hilbert space
摘要: Two settings are considered: flows on finite dimensional Riemannian manifolds,and semiflows on Hilbert spaces with potential applications to dissipative parabolic PDEs. Under certain conditions expressed in terms of Lyapunov exponents and entropy, we prove the existence of dynamical structures called horseshoes which implies in particular the presence of infinitely many periodic solutions. For diffeomorphisms of compact manifolds, analogous results are due to A. Katok. Here we extend Katok's results to (i) continuous time and (ii) infinite dimensions. This is a joint work with Lai-Sang Young at Courant Institute.
时间： 4月18日(周四）下午4:30-5:30
地点： 数学科学学院1611教室

报告人简介： 连增教授是微分方程动力系统领域知名青年数学家，主要研究领域为随机动力系统与无穷维系统光滑遍历理论。先后在国际顶级数学刊物J. Amer. Math. Soc及Mem. Amer. Math. Soc.发表论文，多次受邀在国际重要学术会议上作报告。

主办单位: 中国科学技术大学数学科学学院

        
 
欢迎感兴趣的师生参加!