主講人：陳光淦教授/周林鋒副教授 四川師范大學(xué)/四川大學(xué)
時(shí)間：2022年11月6日14：30
地點(diǎn)：騰訊會(huì)議 233 479 353
舉辦單位：數(shù)理學(xué)院
主講人介紹：陳光淦，1978年生，四川師范大學(xué)數(shù)學(xué)科學(xué)院副院長(zhǎng)、教授、博士生導(dǎo)師。四川省數(shù)學(xué)會(huì)常務(wù)理事，第十二批四川省學(xué)術(shù)和技術(shù)帶頭人后備人選，四川省青年創(chuàng)新團(tuán)隊(duì)帶頭人，美國(guó)《Mathematical Reviews》評(píng)論員，德國(guó)《Zentralblatt Math》評(píng)論員，“四川師范大學(xué)勞動(dòng)模范”稱(chēng)號(hào)獲得者。研究方向是隨機(jī)動(dòng)力系統(tǒng)、隨機(jī)偏微分方程、數(shù)學(xué)物理。先后主持國(guó)家自然科學(xué)基金面上項(xiàng)目2項(xiàng)、國(guó)家自然科學(xué)基金青年基金1項(xiàng)、國(guó)家自然科學(xué)基金天元基金1項(xiàng)，以及四川省科技廳和教育廳重點(diǎn)科研項(xiàng)目多項(xiàng)。在《SIAM Journal on Mathematical Analysis》、《Journal of Functional Analysis》、《Chaos》、《數(shù)學(xué)學(xué)報(bào)》等專(zhuān)業(yè)學(xué)術(shù)期刊上發(fā)表論文20多篇，研究結(jié)果被國(guó)內(nèi)外同行多次引用。2006年、2010年和2021年3次榮獲四川省科學(xué)技術(shù)獎(jiǎng)二等獎(jiǎng)，其中，2021年為獲獎(jiǎng)項(xiàng)目第一完成人。 周林鋒, 副教授、碩士生導(dǎo)師，從事常微分方程與動(dòng)力系統(tǒng)雙曲性問(wèn)題的研究,其工作發(fā)表在J. Differential Equations 和J. Functional Analysis 等國(guó)際數(shù)學(xué)期刊, 主持國(guó)家自然科學(xué)基金青年基金和面上基金, 并參與多項(xiàng)國(guó)家自然科學(xué)基金.
內(nèi)容介紹：
陳光淦教授報(bào)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.
周林鋒副教授報(bào)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?.