Limit Theorems in Dynamical Systems

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The PI will continue his work on limit theorem for dynamical systems. The main directions of research will be the following: convergence to stable laws, limit theorems for actions of higher rank abelian groups, limit theorems for random translations and diffusion limit theorems.Examples of systems which evolve according to deterministic laws but exhibit stochasticity when the initial conditions are not known exactly appear in natural phenomena ranging from atomic scales (Brownian Motion of particles in fluids) to astronomical scales (motion of comets and asteroids). In cases where exact calculations are impossible due to stochasticity a statistical description has to be used. The research supported by the current proposal will develop methods of statistical description of deterministic system by identifying the regions in the phase space responsable for the stochasticity and analyzing the behaviour of the system in those regions. PI will also continue his synergistic activities including organizing conferences, giving lectures and minicourses on recent advances in dynamics, writing survey papers and mentoring graduate students and postdocs.