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[Lecture] Random Perturbations of Integrable Systems and Applications to Chains of Oscillators with Noise
May. 24, 2024

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Speaker: Sergei Kuksin(Université Paris Cité and Sorbonne Université,Steklov MathematicalInstitute of RAS,Peoples' Friendship University of Russia,Shandong University)

Time: 15:30-16:30 p.m., May 24, 2024, GMT+8

Venue: Room 77201, Jingchunyuan #78, BICMR 


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. 

Source: Beijing International Center for Mathematical Research, PKU