Random Perturbations of Integrable Systems and Applications to Chains of Oscillators with Noise
Speaker(s): Sergei Kuksin(Université Paris Cité and Sorbonne Université,Steklov Mathematical Institute of RAS,Peoples' Friendship University of Russia,Shandong University)
Time: 15:30-16:30 May 24, 2024
Venue: Room 77201, Jingchunyuan 78, BICMR
Abstract: I will discuss
stochastic epsilon-perturbations of an 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.
Bio Sketch: Sergei Kuksin is a professor of mathematics at the Université Paris Cité and Sorbonne Université and at Steklov Mathematical Institute of RAS, a head of laboratory in the RUDN University (Moscow) and a professor at the Institute for Financial Studies, Shandong University. His research is the broad area of analysis and probability, including KAM theory, PDEs with randomness, turbulence and statistical hydrodynamics, and elliptic PDEs for functions between compact manifolds. In 1992 he was a plenary speaker with talk "KAM theory for partial differential equations" at the European Congress of European Mathematicians in Paris. In 1998 he was an invited speaker at International Congress of Mathematicians in Berlin. In 2016 he received the Lyapunov Prize of the Russian Academy of Sciences.