Orbit (dynamics) - Definition

Definition

Given a dynamical system (T, M, Φ) with T a group, M a set and Φ the evolution function

where

we define

then the set

is called orbit through x. An orbit which consists of a single point is called constant orbit. A non-constant orbit is called closed or periodic if there exists a t in T so that

for every point x on the orbit.

Read more about this topic:  Orbit (dynamics)

Famous quotes containing the word definition:

    According to our social pyramid, all men who feel displaced racially, culturally, and/or because of economic hardships will turn on those whom they feel they can order and humiliate, usually women, children, and animals—just as they have been ordered and humiliated by those privileged few who are in power. However, this definition does not explain why there are privileged men who behave this way toward women.
    Ana Castillo (b. 1953)

    Scientific method is the way to truth, but it affords, even in
    principle, no unique definition of truth. Any so-called pragmatic
    definition of truth is doomed to failure equally.
    Willard Van Orman Quine (b. 1908)

    The man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.
    William James (1842–1910)