A Hamiltonian may have multiple conserved quantities G i. If the symplectic manifold has dimension 2 n and there are n functionally independent conserved quantities G i which are in involution (i.e., { G i, G j } = 0), then the Hamiltonian is Liouville integrable. The Liouville–Arnold theorem says that, locally, any Liouville integrable Hamiltonian can be transformed via a symplectomorphism into a new Hamiltonian with the conserved quantities G i as coordinates; the new coordinates are called action–angle coordinates. The transformed Hamiltonian depends only on the G i, and hence the equations of motion have the simple form G ˙ ˙ i = 0 , φ φ ˙ ˙ i = F i ( G ) for some function F. There is an entire field focusing on small deviations from integrable systems governed by the KAM theorem.