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:
“We recognize caste in dogs because we rank ourselves by the familiar dog system, a ladderlike social arrangement wherein one individual outranks all others, the next outranks all but the first, and so on down the hierarchy. But the cat system is more like a wheel, with a high-ranking cat at the hub and the others arranged around the rim, all reluctantly acknowledging the superiority of the despot but not necessarily measuring themselves against one another.”
—Elizabeth Marshall Thomas. “Strong and Sensitive Cats,” Atlantic Monthly (July 1994)