Types of Attractors
Attractors are parts of the phase space of the dynamical system. Until the 1960s, as evidenced by textbooks of that era, attractors were thought of as being simple geometrical subsets of the phase space: points, lines, surfaces, volumes. The (topologically) wild sets that had been observed were thought to be fragile anomalies. Stephen Smale was able to show that his horseshoe map was robust and that its attractor had the structure of a Cantor set.
Two simple attractors are the fixed point and the limit cycle. There can be many other geometrical sets that are attractors. When these sets (or the motions on them), are harder to describe than the classical geometric objects, then the attractor is a strange attractor, as described in the section below.
Read more about this topic: Attractor
Famous quotes containing the words types of and/or types:
“Science is intimately integrated with the whole social structure and cultural tradition. They mutually support one otheronly in certain types of society can science flourish, and conversely without a continuous and healthy development and application of science such a society cannot function properly.”
—Talcott Parsons (19021979)
“The wider the range of possibilities we offer children, the more intense will be their motivations and the richer their experiences. We must widen the range of topics and goals, the types of situations we offer and their degree of structure, the kinds and combinations of resources and materials, and the possible interactions with things, peers, and adults.”
—Loris Malaguzzi (19201994)