Ergodic and Statistical Phenomena in Dynamics

Princeton University, Princeton NJ

Investigators

Abstract

PI: Yakov Sinai, Princeton University DMS-0245397 Abstract: The research will go in three different directions: 1] Methods of the theory of dynamical systems for the analysis of solutions of equations of hydrodynamics: The existence problem for the 3D-Navier-Stokes system remains a challenge. The theory of dynamical systems can help to find new directions for research. 2] (3x+1) - problem and other number-theoretic dynamical systems: These are long-standing and easily formulated problems. The goal is to find hidden structures which can help to get a progress in the analysis of typical orbits. 3] Problem of adiabatic piston: It is one of popular problems in non-equilibrium statistical mechanics. Methods from ergodic theory and probability theory can be useful. The theory if dynamical systems is an interdisciplinary branch of mathematics which has many applications in physics, engineering, biology, etc. It is assumed that it will be applied to some problems in hydrodynamics, number theory and non-equilibrium statistical mechanics. In all cases I intend to work on several central problems in each of these cases.