Qualitative and Statistical Theory of Dissipative Systems

Abstract

This series of lectures will be concerned with the statistical theory of dissipative systems and, at least metaphorically, with its applications to hydrodynamics. The principal objective will be to try to clarify the question of hov to construct the appropriate ensemble for the statistical theory of turbulence. We will not, however, come to this point for some time. It should be noted at the outset that the relevance of our discussion to the theory of turbulence is dependent on the guess that, despite the fact that fluid flow problems have infinite-dimensional state spaces, the Important phenomena are essentially finite dimensional.^* This point of view is not universally accepted [4]. On the other hand, the theory is not restricted to fluid flow problems; it also applies to a large number of model systems arising, for example, in mathematical biology [7].