188比分直播

动力系统中的不变流形理论专题报告IV

发布者:文明办发布时间:2022-10-31浏览次数:227


主讲人:陈光淦教授/周林锋副教授 四川师范大学/四川大学


时间:2022年11月6日14:30


地点:腾讯会议 233 479 353


举办单位:数理学院


主讲人介绍:陈光淦,1978年生,四川师范大学数学科学院副院长、教授、博士生导师。四川省数学会常务理事,第十二批四川省学术和技术带头人后备人选,四川省青年创新团队带头人,美国《Mathematical Reviews》评论员,德国《Zentralblatt Math》评论员,“四川师范大学劳动模范”称号获得者。研究方向是随机动力系统、随机偏微分方程、数学物理。先后主持国家自然科学基金面上项目2项、国家自然科学基金青年基金1项、国家自然科学基金天元基金1项,以及四川省科技厅和教育厅重点科研项目多项。在《SIAM Journal on Mathematical Analysis》、《Journal of Functional Analysis》、《Chaos》、《数学学报》等专业学术期刊上发表论文20多篇,研究结果被国内外同行多次引用。2006年、2010年和2021年3次荣获四川省科学技术奖二等奖,其中,2021年为获奖项目第一完成人。 周林锋, 副教授、硕士生导师,从事常微分方程与动力系统双曲性问题的研究,其工作发表在J. Differential Equations 和J. Functional Analysis 等国际数学期刊, 主持国家自然科学基金青年基金和面上基金, 并参与多项国家自然科学基金.


内容介绍:

陈光淦教授报告摘要:This talk is concerned with the dynamics of a slow–fast stochastic evolutionary system quantified with a scale parameter. An invariant foliation decomposes the state space into geometric regions of different dynamical regimes, and thus helps understand dynamics. A slow invariant foliation is established for this system. It is shown that the slow foliation converges to a critical foliation (i.e., the scale parameter is zero) in probability distribution, as the scale parameter tends to zero. The approximation of slow foliation is also constructed with error estimate in distribution. Furthermore, the geometric structure of the slow foliation is investigated: every fiber of the slow foliation parallels each other, with the slow manifold as a special fiber. In fact, when an arbitrarily chosen point of a fiber falls in the slow manifold, the fiber must be the slow manifold itself. This work is jointed with Prof. Jinqiao Duan and Prof. Jian Zhang. 

周林锋副教授报告摘要:Nonuniform exponential dichotomy describes nonuniform hyperbolicity for linear dynamical systems. In this talk, I will introduce our works on the relationship between nonuniform exponential dichotomies and admissibility of function classes, and the persistence of nonuniformly normally hyperbolic invariant manifolds joint with Weinian Zhang, Kening Lu and Davor Dragi?evi?.