There are many different types of motion that can be exhibited by a dynamical system. The simplest is fixed point behavior, which can be seen in a pendulum when friction and gravity bring the system to a halt. Most fixed points can be likened to a ball placed on top of a hill, which rolls downward until at some point the ball sits on a flat spot and has no momentum to carry it further. The next simplest type of motion is known as a limit cycle or periodic motion, which involves movement that repeats itself over and over. A lone planet orbiting a star in an elliptical orbit is an example of a limit cycle.
Some limit cycles are more complicated than others.
For example, a child on a swing drives the motion of the swing by periodically rocking in beat with the natural frequency of the swing, much like an idealized pendulum. Now, if the child rhythmically swings one leg at a higher frequency, the motion of that leg will cause the motion of his or her body to subtly wobble back and forth. If it is timed accurately, the child may be able to coerce the motion into behavior that is more complicated than that of the planet, with his or her body moving back and forth along the main axis of the swing, and perpendicularly left to right in step with the leg. A slightly more complicated form of motion is found in quasiperiodic systems, which are similar to periodic systems except that they never quite repeat themselves. For example, the moon orbits Earth, which orbits the sun, which, in turn, orbits the galactic center, and so on.