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:

    No man, not even a doctor, ever gives any other definition of what a nurse should be than this—”devoted and obedient.” This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.
    Florence Nightingale (1820–1910)

    One definition of man is “an intelligence served by organs.”
    Ralph Waldo Emerson (1803–1882)

    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)