Some properties of the simple nonlinear recursion $y(\mathrm{\ell }+1)=[1-y(\mathrm{\ell }){]}^p$ with $p$ an arbitrary positive integer

It is shown that the behavior of the solutions of the nonlinear recursion $y(\mathrm{\ell }+1)=[1-y(\mathrm{\ell }){]}^p$ – where the dependent variable $y(l)$ is a real number, $\mathrm{\ell }=0;1;\mathrm{2...}$ is the independent variable, and $p$ is an arbitrary positive integer – is easily ascertainable.