主讲人简介：
Alexandre Carvalho教授现任巴西圣保罗大学教授，师从无穷维动力系统奠基人之一J. K.Hale教授，2012年当选为巴西科学院院士。长期活跃在国际学术前沿，与合作者撰写的专著“Attractors for infinite-dimensional non-autonomous dynamical systems”，Springer-Verlag(2013)，已成为无穷维动力系统领域经典教材。已经发表学术论文110余篇。发表的杂志包括Transactions of the American Mathematical Society、Communicationsin Partial Differential Equations、Indiana University Mathematics Journal、Siam Journal of Mathematical Analysis、Journal of Differential Equations、ErgodicTheory & Dynamical Systems、Nonlinearity等国际著名期刊。现任Journal of DifferentialEquations、Journal of Dynamics and Differential Equations等多个国际学术刊物的编委。
内容摘要：
In this lecture, we show that certain Morse–Smale dynamical systems defined on Hilbert spaces exhibit the Lipschitz Shadowing property on their global attractors and Hölder Shadowing property in a neighborhood of the attractor. This result extends classical theorems on shadowing for dynamical systems on compact manifolds to the infinite-dimensional setting. We also discuss applications, including results on the continuity of attractors and the stability of infinite-dimensional Morse–Smale systems.
