Systems of this type have a number of independent conserved quantities equal to the number of their degrees of freedom, and in these systems, the mutual Poisson brackets of the conserved quantities all vanish.
In driven systems that are not of this type, the stable and unstable manifolds do not coincide. A distinctive feature of these systems is the presence of continuous families of periodic orbits, a consequence of the Poincare-Birkhoff theorem, and systems of this type also admit equilibrium and quasiperiodic orbits. The term describing these systems is also used to describe constraints which can be written in terms of the derivative of a coordinate constraint and the classical form of the KAM theorem concerns the stability of perturbations to Hamiltonian systems of this type. Systems of this type have a number of independent conserved quantities equal to the number of their degrees of freedom, and in these systems, the mutual Poisson brackets of the conserved quantities all vanish. A canonical example of such a system is a periodically driven amplitude with small drive amplitude. For 10 points, identify these types of dynamical systems, so named because they admit direct solutions by anti-derivatives.
In driven systems that are not of this type, the stable and unstable manifolds do not coincide.
{integrable} systems [prompt on "{Hamiltonian}" {systems}]