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.

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