Properties of the entropies at weak intermittent states of Lorenz-type systems

The particular chaotic states of Lorenz-type systems are studied when a marginally unstable fixed point is approached by typical trajectories. By analytically investigating a two-dimensional Poincar\'e map it is shown that these states have a number of interesting properties. They can be weakly or strongly intermittent. In the weak intermittent cases a phase-transition-like phenomenon occurs in the R\'enyi entropies, and power-law decay of the truncated Kolmogorov-Sinai entropy is found.