报告人：Douglas Duarte Novaes
报告地点：ZOOM会议ID：223 258 3672，密码：251204
报告时间：2025年12月18日星期四19:00-20:00
邀请人：冀书关、邢佳敏
报告摘要：
Invariant compact manifolds, such as equilibria, periodic orbits, and invariant tori, provide important information about the dynamics of differential systems. This knowledge is significantly increased when we can describe the behavior of nearby trajectories. In this talk, we present conditions that ensure the existence of invariant tori in perturbed differential systems, along with results on their regularity, stability, and dynamics. These conditions are based on higher-order averaged equations and extend classical theorems by Krylov, Bogoliubov, Mitropolsky, and Hale. As an application, we also explore a three-dimensional version of Hilbert's 16th Problem, focusing on the number of isolated invariant tori in 3D polynomial vector fields.
主讲人简介：
Douglas D. Novaes holds a Bachelor's degree (2010), a Master's degree (2012), and a PhD (2015) in Mathematics from the Universidade Estadual de Campinas (Unicamp), including a research internship at the Universitat Autònoma de Barcelona in 2014 as part of his doctoral training. Postdoctoral fellow at Unicamp and at the Universitat Autònoma de Barcelona in 2015, 2016. Since 2016, he has been a faculty member at Unicamp, where he earned the Livre-Docência (habilitation) in 2019 and currently holds an Associate Professor (MS-5.2) position. He is also an Affiliate Member of the Brazilian Academy of Sciences. His research lies in the area of Dynamical Systems, with a focus on bifurcation theory and nonsmooth dynamical systems.
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