Estimation of Markers Distributions Near the Virtual K-Plane

Estimation of Markers Distributions Near the Virtual K-Plane 

Apparently, somewhere near the unstable K-plane, the system has one or two stable ones, the latter acting as attractors and gathering aU markers initially located at the virtual K-plane. As shown above, a case when there is only one unstable K-plane may be observed. Then the initial distribution of markers simply sprawls out (the system gradually forgets the initial contact plane). 

Let Ax be the distance between two markers near the virtual K-plane (for which (dU/dx) 0). The relative velocity of these markers is roughly equal (for small Ax) to 

The composition of each (even virtual) K-plane must remain constant therefore. 

Let Axo be the initial distance between the markers. Then, formally, we may write Ax (t) 

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