ABSTRACT
A trajectory on a chaotic attractor can go in any of many directions. It can also visit some zones on the attractor often and others rarely. The similarity dimension, capacity, and Hausdorff dimension consider only the geometry of the attractor (its apparent size and shape). They make no attempt to account for the frequency at which a trajectory visits different regions on the attractor. The next two measures-the information dimension and the correlation dimension-try to reflect not only the attractor' s geometry but also the frequency with which the system gets to various phase space sectors.
