Chaotic phenomena in three settings: large, noisy and out of equilibrium

Three directions of research are proposed. The first two concern the creation, detection and calibration of chaos in (1) high or infinite dimensional systems and (2) stochastically perturbed systems. It is suggested that existing ideas from parts of (finite dimensional) hyperbolic theory be extended to these settings. The third topic has a statistical mechanics flavour. A better understanding of nonequilibrium steady states of chaotic Hamiltonian models is sought. (open problem)