Basic Definitions
A dynamical system is a manifold M called the phase (or state) space endowed with a family of smooth evolution functions Φt that for any element of t ∈ T, the time, map a point of the phase space back into the phase space. The notion of smoothness changes with applications and the type of manifold. There are several choices for the set T. When T is taken to be the reals, the dynamical system is called a flow; and if T is restricted to the non-negative reals, then the dynamical system is a semi-flow. When T is taken to be the integers, it is a cascade or a map; and the restriction to the non-negative integers is a semi-cascade.
Read more about this topic: Dynamical System
Famous quotes containing the words basic and/or definitions:
“Surrealism is not a school of poetry but a movement of liberation.... A way of rediscovering the language of innocence, a renewal of the primordial pact, poetry is the basic text, the foundation of the human order. Surrealism is revolutionary because it is a return to the beginning of all beginnings.”
—Octavio Paz (b. 1914)
“What I do not like about our definitions of genius is that there is in them nothing of the day of judgment, nothing of resounding through eternity and nothing of the footsteps of the Almighty.”
—G.C. (Georg Christoph)