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:

    “It’s a rare parent who can see his or her child clearly and objectively. At a school board meeting I attended . . . the only definition of a gifted child on which everyone in the audience could agree was “mine.””
    —Jane Adams (20th century)

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

    “... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.”
    —George Eliot [Mary Ann (or Marian)