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On the eventual periodicity of xn+1=max{1xn,Anxn−1} with a ..:

Feuer, J. ; McDonnell, K.T.
Computers & Mathematics with Applications.  56 (2008)  4 - p. 883-890 , 2008
Link: https://doi.org/10.1016/j.camwa.2008.01.018