Chapter 1: Periodic and Chaotic Oscillators

Chaotic behavior is intimately intertwined with the three-body problem. In celestial mechanics we treat the energy as a conserved quantity because dissipation is negligible since the planets move in a very high vacuum. This is very rarely observed for phenomena that occur on the earth (there is always friction somewhere): systems dissipate energy through heat. The trajectories of such systems are “attracted” to certain regions in their state spaces: these regions correspond to the existence of attractors of the type that we will encounter with the damped pendulum. In this case the attractor is a simple point in the state space that defines a stable state of rest (zero angle, zero angular velocity). There exist much more interesting situations in which the attractor is more complicated (chaotic, for example)…