Statistical properties of turbulence

It is now convenient to reexamine some questions of fundamental nature with the purpose of analyzing the possible consequences of Ruelle’s principle introduced in §5.7. We shall make frequently reference to the general description of motions given in Chap. 5 in a context in which we imagine that the considered motions are attracted by some attracting set in phase space, which will have zero volume when energy dissipation occurs in the system. The main purpose of this section and of the following ones is to analyze consequences of Ruelle’s principle, see §5.7, with particular attention to fluid motions.