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Left panel: In red the map x′ = x + u exp(−x) (f*(x) with z = →∞ and u = 0.1). In blue the trajectory xt = ln[exp x0 + ut] initiated at x0 = −1. Its positions approximate asymptotically (minus) the reciprocals of the Factorial numbers. Right panel: In red the map x′ = x + u exp x (f*(x) with Z → −∞, 0 ≤ u ≤ 1). In blue the trajectory xt = −ln[exp(−x0) + ut] initiated at x0 = 1. Its positions approximate asymptotically the Factorial numbers. Identity lines in green.
