Random and Stochastic Dynamical Systems

The goal of the present project is to understand dynamics of the systems whose evolution laws change with time. The research is concentrated on random dynamical systems where the evolution rules of the system change randomly: such systems play important role in many settings from artificial intelligence to ocean dynamics. The recent advances in artificial intelligence will accelerate the research. The project will study the appearance of chaotic behavior and to devise the tools of statistical treatment of systems at hand. The project also includes the training of graduate students and early-career researchers working in dynamical systems. The main theme of the project is to understand non stationary dynamical systems by combining the tools from dynamical systems, probability and analysis. Recent developments in the theory of systems with non zero Lyapunov exponents and harmonic analysis will be used to study both path-wise behavior of random dynamical systems and to understand the evolution of adiabatic invariants for small perturbation of Hamiltonian systems. Both deterministic and random perturbations will be analyzed. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.