Chaotic Dynamics
In common usage, "chaos" means "a state of disorder". However, in chaos theory, the term is defined more precisely. Although there is no universally accepted mathematical definition of chaos, a commonly used definition says that, for a dynamical system to be classified as chaotic, it must have the following properties:
- it must be sensitive to initial conditions;
- it must be topologically mixing; and
- its periodic orbits must be dense.
The requirement for sensitive dependence on initial conditions implies that there is a set of initial conditions of positive measure which do not converge to a cycle of any length.
Read more about this topic: Chaos Theory
Famous quotes containing the words chaotic and/or dynamics:
“The attitude that nature is chaotic and that the artist puts order into it is a very absurd point of view, I think. All that we can hope for is to put some order into ourselves.”
—Willem De Kooning (b. 1904)
“Anytime we react to behavior in our children that we dislike in ourselves, we need to proceed with extreme caution. The dynamics of everyday family life also have a way of repeating themselves.”
—Cathy Rindner Tempelsman (20th century)