Abstract
In this paper we discuss the relation between the structures of the series expansion for the Dragt and Finn composition of Lie transforms and for a transformation introduced by Giorgilli and Galgani. A recursive algorithm is presented which is used to generate the series expansion for the composition of Lie transforms. This algorithm strongly resembles the algorithm of Giorgilli and Galgani, and differs from it only in an ordering property. The relation with the algorithms of Kamel and Henrard for Deprit's direct and inverse series is also discussed.
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References
Deprit, A.: 1969, Celestial Mechanics 1, 12–30.
Kamel, A. A.: 1969, Celestial Mechanics 1, 190–199.
Henrard, J.: 1970, Celestial Mechanics 3, 107–120.
Henrard, J.: 1973, ‘The algorithm of the inverse for Lie transform’, in Recent Advances in Dynamical Astronomy, B. D. Tapley and V. Szebehely (eds.), pp. 250–259, Reidel, Dordrecht.
Dragt, A. and Finn, J. M.: 1976, J. Math. Phys. 17, 2215–2227.
Giorgilli, A. and Galgani, L.: 1978, Celestial Mechanics 17, 267–280.
Giorgilli, A. and Galgani, L.: 1985, Celestial Mechanics 37, 95–112.
Rapaport, M.: 1982, Celestial Mechanics 28, 291–293.
Fassò, F. and Benettin, G.: 1989, J. Appl. Math. Phys. (ZAMP) 40, 307–329.
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Fassò, F. On a relation among lie series. Celestial Mech Dyn Astr 46, 113–118 (1989). https://doi.org/10.1007/BF00053041
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DOI: https://doi.org/10.1007/BF00053041