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:
“Was man made stupid to see his own stupidity?
Is God by definition indifferent, beyond us all?
Is the eternal truth man’s fighting soul
Wherein the Beast ravens in its own avidity?”
—Richard Eberhart (b. 1904)
“The very definition of the real becomes: that of which it is possible to give an equivalent reproduction.... The real is not only what can be reproduced, but that which is always already reproduced. The hyperreal.”
—Jean Baudrillard (b. 1929)
“Beauty, like all other qualities presented to human experience, is relative; and the definition of it becomes unmeaning and useless in proportion to its abstractness. To define beauty not in the most abstract, but in the most concrete terms possible, not to find a universal formula for it, but the formula which expresses most adequately this or that special manifestation of it, is the aim of the true student of aesthetics.”
—Walter Pater (1839–1894)