**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

### Other articles related to "chaotic, chaotic dynamics":

... A nonlinear dynamical system exhibits

**chaotic**hysteresis if it simultaneously exhibits

**chaotic dynamics**(chaos theory) and hysteresis ... If

**chaotic dynamics**appear either prior to or just after such jumps, or are persistent throughout each of the various equilibrium states, then the system is said to exhibit ...

**Chaotic dynamics**are irregular and bounded and subject to sensitive dependence on initial conditions ...

### Famous quotes containing the words dynamics and/or chaotic:

“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)

“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)