New graphical method for the iteration of one-dimensional maps (Q1107270)

We present the ``inverse-curve method'' which (1) simplifies a graphical iteration of the logistic map by avoiding the use of the diagonal; (2) naturally demonstrates the first period-doubling bifurcation; and (3) allows one to read immediately the stable pair of the two-point cycle off from the graph of the recursive function. Cycles of order \(m\geq 2\) are reduced to graphs of k- and \(\ell\)-iterate functions with \(k+\ell =m\). The method can easily be applied to other one-dimensional maps with more complicated recursion relations.