Pavlenko, Yu. G.; Zelenskij, S. I. Using a dual variable method to integrate non-Hamiltonian systems. (English. Russian original) Zbl 0627.70014 Mosc. Univ. Phys. Bull. 42, No. 1, 7-12 (1987); translation from Vestn. Mosk. Univ., Ser. III 28, No. 1, 8-13 (1987). 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. Reviewer: W.Sarlet MSC: 70H05 Hamilton’s equations 37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems Keywords:perturbation analysis; multiple integration of nested Poisson brackets PDFBibTeX XMLCite \textit{Yu. G. Pavlenko} and \textit{S. I. Zelenskij}, Mosc. Univ. Phys. Bull. 42, No. 1, 7--12 (1987; Zbl 0627.70014); translation from Vestn. Mosk. Univ., Ser. III 28, No. 1, 8--13 (1987)