Merger of chaotic bands in period-doubling cascades (Q1187013)

Considering a 1-dimensional difference equation \(x_{x+1}=F(x_ n,\lambda)\) the author describes the reverse bifurcation of chaotic bands for \(\lambda > \lambda_ \infty\), where \(\lambda_ \infty\) is the limit of Feigenbaum sequence. More precisely, when \(\lambda\) decreases from the parameter value \(\lambda_{M_ 0}\) to \(\lambda_ \infty\) one chaotic band splits into two bands at \(\lambda_{M_ 0}\), and two chaotic bands split into \(2^ 2\) bands at \(\lambda_{M_ 1}\), etc. The resulting sequence \((\lambda_{M_ i})\) converges decreasingly to the critical value \(\lambda_ \infty\). Precise values of the parameters \(\lambda_{M_ 0}\) and \(\lambda_{M_ 1}\) are determined.