Period Doubling and Stable Orbits

Abstract

Several authors have noticed that numerical simulations of the Lorenz equations indicate the existence of stable periodic orbits in some intervals of r-values. This behaviour is quite different from the behaviour discussed in Chapter 3, since for r-values near 28.0 we saw no stable periodic orbits, and had strong arguments that none could exist. We will attempt to reconcile the two phenomena in Chapter 5.