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:
“Our chaotic economic situation has convinced so many of our young people that there is no room for them. They become uncertain and restless and morbid; they grab at false promises, embrace false gods and judge things by treacherous values. Their insecurity makes them believe that tomorrow doesn’t matter and the ineffectualness of their lives makes them deny the ideals which we of an older generation acknowledged.”
—Hortense Odlum (1892–?)
“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)