Dynamical System (definition) - Compactification of A Dynamical System

Compactification of A Dynamical System

Given a global dynamical system (R, X, Φ) on a locally compact and Hausdorff topological space X, it is often useful to study the continuous extension Φ* of Φ to the one-point compactification X* of X. Although we lose the differential structure of the original system we can now use compactness arguments to analyze the new system (R, X*, Φ*).

In compact dynamical systems the limit set of any orbit is non-empty, compact and simply connected.

Read more about this topic:  Dynamical System (definition)

Famous quotes containing the word system:

    Delight at having understood a very abstract and obscure system leads most people to believe in the truth of what it demonstrates.
    —G.C. (Georg Christoph)