14 Pages

informal review of the mathematical concepts

detailed, earlier

The possible equilibrium states of the system as we have seen, are obtained as the minima of some function f, and they form a surface - often called a manifold - in n + k dimensional space, where n is the dimension of the state space (the nunber of ~-variables) and k the dimension of the control state (the nunber of ~-variables). The behaviour of the system is described by trajectories on the manifold and hence our interest in the geometry, or more generally, the topology, of this surface.