Thus, the time evolution of a function f on a symplectic manifold can be given as a one-parameter family of symplectomorphisms (i.e., canonical transformations, area-preserving diffeomorphisms), with the time t being the parameter: Hamiltonian motion is a canonical transformation generated by the Hamiltonian. That is, Poisson brackets are preserved in it, so that any time t in the solution to Hamilton's equations, q ( t ) = exp ⁡ ⁡ ( − − t { H , ⋅ ⋅ } ) q ( 0 ) , p ( t ) = exp ⁡ ⁡ ( − − t { H , ⋅ ⋅ } ) p ( 0 ) , can serve as the bracket coordinates. Poisson brackets are canonical invariants.