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Left panel: In red the map x′ = x/(1 − x) (f*(x) with z = 2 and u = 1). In blue the trajectory xt = −1/(1 + t) initiated at x0 = −1. Its positions are (minus) the reciprocals of Natural numbers. Right panel: In red the map x′ = x + 1 (f*(x) with Z = 0 and u = 1). In blue the trajectory xt = 1 + t initiated at x0 = 1. Its positions are the Natural numbers. Identity lines in green.
