Abstract:
I will discuss long-time behaviour in dynamical systems with random forces in finite and infinite-dimensional phase spaces and present recent results of A. Shirikyan and myself on existence for such systems of statistical equilibria with attracting distributions of all solutions as time goes to infinity. The novelty of our work is that we do not assume that the values of the random forces in different instants of time are independent. Accordingly, the random dynamics, defined by the systems we consider, is not Markovian. In my talk I will try to present the crucial ideas of our proof.
Biography:
Sergei Kuksin is a Directeur de Recherche at Université Paris Cité, Sorbonne Université, and Head Scientist at the Steklov Mathematical Institute of RAS. He received his PhD from Moscow State University and has been a Professor at Heriot-Watt University and Directeur de Recherche at École Polytechnique. He did pioneering work in the development of KAM theory for PDEs, ergodic theory of randomly forced PDEs, as well as averaging of Hamiltonian PDEs perturbed by a damping term and a random force. In 1992, he was a plenary speaker at the European Congress of Mathematics in Paris. In 1998, he was an invited speaker at the International Congress of Mathematicians in Berlin. In 2016, he received the Lyapunov Prize of the Russian Academy of Sciences.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai
This event is open to the NYU Shanghai community and Math community.