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Mathematical Problems in Engineering
Volume 2015, Article ID 982857, 10 pages
Research Article

A Note about Certain Arbitrariness in the Solution of the Homological Equation in Deprit’s Method

1Scientific Computing Group (GRUCACI), University of La Rioja, 26004 Logroño, Spain
2Center for Biomedical Research of La Rioja (CIBIR) and Scientific Computing Group (GRUCACI), 26006 Logroño, Spain

Received 1 September 2014; Accepted 2 January 2015

Academic Editor: Jun Jiang

Copyright © 2015 Juan Félix San-Juan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Deprit’s method has been revisited in order to take advantage of certain arbitrariness arising when the inverse of the Lie operator is applied to obtain the generating function of the Lie transform. This arbitrariness is intrinsic to all perturbation techniques and can be used to demonstrate the equivalence among different perturbation methods, to remove terms from the generating function of the Lie transform, or to eliminate several angles simultaneously in the case of having a degenerate Hamiltonian.