We have a chaotic system with multiple attractors and, Tomas has argued, an almost
infinite phase space.
The Earth system has a far more complex state topology and
an infinite phase space.
General relativity plays an essential role because
its infinite phase space will prevent cosmic history being simply a repetitive sequence of returns to the same state.
Not exact matches
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.
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.
As someone who has training in both engineering and environmental science — I expect that there are a practically
infinite number of fudge factors that can be used to constrain the size of the
phase space.
Tomas informs me that the Tim Palmer
phase space dV is of practically
infinite size.