Quantities describing local properties of chaotic attractors

We numerically investigate the Local Divergence Rate (LDR) of the Hénon-map. We find that there exists a unique smooth LDR on the Hénon-attractor; locally expanding and contracting parts alternate regularly. Our concept leads to the definition of what we call “fully developed chaos”. Distribution functions (histograms) and auto-correlation functions for different dynamical behavior are computed. Our results indicate that the LDR may be a continuous function on the space in which the attractor is embedded.