This is a single problem for those who are eager and ambitious.


The general  first order quadratic difference equation is

          u(n+1)=  A u(n)^2 + B u(n) +  C.

Show that a change of variables of the form  v(n) = alpha u(n) + beta,

where A, B, C, alpha, beta are constants will turn this arbitary quadratic
equation into one of the form

            v(n+1) = p v(n) ( 1 - v(n)).

Clearly alpha, beta and p are determined by A, B and C.