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

Abstract

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, $\ell =0;1;\mathrm{2...}$ is the independent variable, and $p$ is an arbitrary positive integer -- is easily ascertainable.