4. Stability and Long-Time Behavior

Dynamical systems theory aims at an understanding and comprehension of the complete dynamical system not just at documenting the properties of a particular solution. Essential elements of such a comprehension are the stability of orbits and limiting sets. The stability of orbits addresses the question of whether or not two orbits that start out close together stay close together or eventually diverge from each other. Limiting sets address the question of the long-term behavior of non-periodic orbits.