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

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