Lyapunov-exponent spectra for the Lorenz model

Abstract

Using a fast algorithm we have calculated the Lyapunov exponents at about 6000 parameter points in the range $0.1<r<520$, $\ensuremath{\sigma}=10$, and $b=\frac{8}{3}$ of the Lorenz model. In the chaotic region we find a large number of narrow windows containing periodic orbits---somewhat similar to what is the case in the one-dimensional logistic map.