Colloquium on April 18th, 2005MartinGutzwillerFellowship, Award CeremonyAntonio Politi Dynamics of highdimensional systems: From a microscopic to a macroscopic description Systems with many degrees of freedom such as lattices, networks, and fluids may exhibit a nontrivial macroscopic behaviour, especially when brought out of equilibrium. The question I wish to address is whether Lyapunov exponents (i.e. the dynamics of infinitesimal perturbations) which are so effective in characterizing lowdimensional chaos are also useful in capturing the relevant features of macroscopic dynamics. Some models (typically globally coupled systems) suggest that microscopic macroscopic worlds are separated from one another. Finiteamplitude Lyapunov exponents appear to be the right tool to analyse the dyanamics of such systems on different observational scales. The numerical analysis of some other systems (e.g. 2d fluids) suggest instead that the dynamics of weakly unstable Lyapunov "modes" conveys  

