  But did a realistic model of a system ever meet the condition of metric indecomposability? What is needed to derive metric indecomposability is sufficient instability of the trajectories so that the trajectories do not form groups of non-zero measure which fail to wander sufficiently over the entire phase region. The existence of a hidden constant of motion would violate metric indecomposability. After much arduous work, culminating in that of Ya. Sinai, it was shown that some “realistic” models of systems, such as the model of a gas as “hard spheres in a box,” conformed to metric indecomposability. On the other hand another result of dynamical theory, the Kolmogorov-Arnold-Moser (KAM) theorem shows that more realistic models (say of molecules interacting by means of “soft” potentials) are likely not to obey ergodicity in a strict sense. In these cases more subtle reasoning (relying on the many degrees of freedom in a system composed of a vast number of constituents) is also needed.