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:

    ... if, as women, we accept a philosophy of history that asserts that women are by definition assimilated into the male universal, that we can understand our past through a male lens—if we are unaware that women even have a history—we live our lives similarly unanchored, drifting in response to a veering wind of myth and bias.
    Adrienne Rich (b. 1929)

    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)

    Mothers often are too easily intimidated by their children’s negative reactions...When the child cries or is unhappy, the mother reads this as meaning that she is a failure. This is why it is so important for a mother to know...that the process of growing up involves by definition things that her child is not going to like. Her job is not to create a bed of roses, but to help him learn how to pick his way through the thorns.
    Elaine Heffner (20th century)