Barkley_Rosser comments on Probability is Subjectively Objective - Less Wrong
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Gotta have that continuous support too, which is the real key to converging on a cycle rather than a point.
In the fuzzier world of not a definite for-real underlying distribution, I note that multiple equilibria or basins in dynamical systems can give the multi-modality that within a herding framework can lead to some sort of cycle in bouncing back and forth between the dominant states.