ABSTRACT
The attractors will be interpreted as minimal attractors. The natural generalization of the notion of an attractor is weaker requirements of attraction, almost everywhere or on the set of the positive Lebesgue measure. Usually in numerical experiments, there is observed an attractor. The notion of B-attractor is mostly used in the theory of dimension, where the coverings of invariant set by balls are considered. Similar to the autonomous systems, for the analysis and visualization of a perturbed dynamical system, one can consider extended phase space and introduce various notions of attractors. One of the basic characteristics of a strange attractor is the sensitivity of its trajectories to the initial data. In computer experiments, it often happens that the trajectories, situated on the unstable manifold of a saddle singular point, everywhere densely fill the B-attractor. This can be observed on the B-attractor of the Lorenz system.
