For the recursion y_{n+1}=(1-y_n)^p with p a positive integer, real solutions are either asymptotically 2-periodic between 0 and 1 or diverge, depending on the initial value.
Solvable nonlinear systems of 2 recursions displaying interesting evolutions
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abstract
In this paper a class of simple, but nonlinear, systems of recursions involving $2$ dependent variables $x_{j}\left( n\right) $ is identified, such that the solutions of their initial-values problems -- with arbitrary initial data $x_{j}\left( 0\right) $ -- may be explicitly obtained.
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Some properties of the simple nonlinear recursion $y(\ell + 1) = [1-y(\ell)]^p$ with $p$ an arbitrary positive integer
For the recursion y_{n+1}=(1-y_n)^p with p a positive integer, real solutions are either asymptotically 2-periodic between 0 and 1 or diverge, depending on the initial value.