報告題目：Random perturbations of integrable systems and applications to chains of oscillators with noise
報 告 人： Sergei Kuksin 教授
所在單位： 1.巴黎城市大學 2.巴黎索邦大學2. 莫斯科斯捷克洛夫數學研究所，3. 俄羅斯人民友誼大學，4. 山東大學金融研究院
報告時間：2024年5月11日 星期六 下午14:00-15：00
報告地點：數學樓第二報告廳
校内聯系人：許璐 xulu@jlu.edu.cn
報告摘要： I will discuss stochastic epsilon-perturbations of an integrable integrable Hamiltonian system in R^{2n}. I will show that, firstly, on time intervals of order 1/epsilon the actions of solutions for perturbed equations are close to those of solutions for specially constructed effective stochastic equations, independent from epsilon. Secondly, if the effective equation is mixing, then the approximation of actions of solutions for perturbed equations, provided by this equation, is uniform in time. All imposed restrictions admit easy sufficient conditions. I will discuss applications of the obtained results to perturbations of chains of nonlinear oscillators, related to the problem of describing the heat conduct in crystals.
報告人簡介：Sergei Kuksin is a head scientist at the Steklov Mathematical Institute, the head of laboratory at the Mathematical Institute of the RUDN University, a senior researcher at Université Paris Cité and Sorbonne Université and a “high level talents” professor of Shandong University. His research deals with KAM theory in PDEs, PDEs involved with random perturbations, turbulence and statistical hydrodynamics, and elliptic PDEs for functions between compact manifolds.
In 1992 he was a plenary speaker at ECM in Paris. In 1998 he was an invited speaker at ICM in Berlin. He received the Lyapunov Prize from the Russian Academy of Sciences.
