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$\begingroup$ What is the source of this question, please? $\endgroup$– Gerry MyersonCommented Oct 21, 2021 at 22:45
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$\begingroup$ It is a dynamics that came up in a setting I encountered. In fact, I wonder whether this process has been studied, perhaps in the literature of dynamical systems. $\endgroup$– pi66Commented Oct 22, 2021 at 5:27
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