What is a Hamiltonian Chaos?
The transition to chaos for a Hamiltonian (conservative) system is somewhat different than that for a dissipative system (recall [2.5]). In an integrable (nonchaotic) Hamiltonian system, the motion is “quasiperiodic”, that is motion that is oscillatory, but involves more than one independent frequency (see also [2.12]). Geometrically the orbits move on tori, i.e. the mathematical generalization of a donut. Examples of integrable Hamiltonian systems include harmonic oscillators (simple mass on a spring, or systems of coupled linear springs), the pendulum, certain special tops (for example the Euler and Lagrange tops), and the Kepler motion of one planet around the sun. It was expected that a typical perturbation of an integrable Hamiltonian system would lead to “ergodic” motion, a weak version of chaos in which all of phase space is covered, but the Lyapunov exponents [2.11] are not necessarily positive. That this was not true was rather surprisingly discovered by one of the first compu
