Chaos and fractals
Early in the last century, Henri Poincaré studied the three-body problem and found very complicated orbits. In this and other systems, he found that after a transient period, classical motion assumes one of four forms:
1 periodic (a limit cycle),
2 steady or damped or stopped,
3 quasi-periodic (more than one frequency),
Example 18.1 (Duffing’s equation) If one attaches a thin piece of iron to the end of a rod that moves sinusoidally in the x direction at frequency ω near two magnets then the x coordinate ...