The famous Lorenz attractor is an exemple of such an invariant set in a 3
dimensional phase space (because the system is described by 3 ODE).
In any case the end result of this trick or insight is that this specific flow is reduced from the infinite
dimensional phase space to a finite 3D space and can be described by only 3 non linear ODE.
Fig. 2: Intermediate result of phasegram generation: Embedding of the analyzed data (blue) in a so - called two -
dimensional phase space.
Portions of the analyzed measurement data are embedded in a so - called two -
dimensional phase space (Fig. 2) at equally spaced time intervals, using a mathematical method that has been described 30 years ago.
Not exact matches
With one position and one velocity coordinate, the
phase space becomes two -
dimensional, so the flow preserves area.
The problem for spatio - temporal chaos is that its «
phase space» is infinite
dimensional so that you can't define dV.
The state (
phase)
space is infinite
dimensional.