学术报告I

报告题目：Lyapunov exponents and Multiplicative Ergodic Theorem for Random Dynamical Systems in Separable Banach spaces

报告人：连增 教授 （英国拉夫堡大学）

报告时间：2015 年 10 月 15日（星期四）上午 9:00-10:00

报告地点：创新园大厦 A1101

校内联系人：柳振鑫 教授       联系电话：84708351-8022

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 seminar talk, I will report both the result and the framework of the proof. This is a joint work with Kening Lu at BYU.

学术报告II

报告题目：Lyapunov exponents, periodic orbits, and horseshoe for semiflows in Hilbert space

报告人：连增 教授 （英国拉夫堡大学）

报告时间：2015 年 10 月 15日（星期四）上午 10:00-11:00

报告地点：创新园大厦 A1101

校内联系人：柳振鑫 教授       联系电话：84708351-8022

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 impliesin 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.