Using a dual variable method to integrate non-Hamiltonian systems (Q1092690)

The main theme of this note is the rather well known property that every first-order system of differential equations can be cast into a Hamiltonian form by a straightforward procedure which requires doubling the number of variables. For the subsequent construction of solutions through a perturbation analysis, the authors here rely on a specific formula involving multiple integration of nested Poisson brackets. The technique is applied to a number of differential equations which define various special functions.