Symmetries of Dynamical Equations

This lecture covers the concept of symmetries in dynamical equations, focusing on the restoration of symmetries at high Reynolds numbers. The instructor discusses the symmetries of the Navier-Stokes equations and their implications for turbulence. Examples include overdamped particles in quadratic potentials and the preservation of symmetry in time evolution. The lecture emphasizes the importance of symmetry considerations in understanding fluid dynamics and highlights the significance of invariant subspaces. Various equations and hypotheses related to symmetry restoration are explored, providing insights into the fundamental principles governing fluid motion.