Editing Dynamical system (section)

==== Compactification of a dynamical system ====
Given a global dynamical system ('''R''', ''X'', Φ) on a [[locally compact]] and [[Hausdorff space|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 space|compact]] and [[simply connected]].