The Equivalence of the Generators of Deprit’s and Giorgelli-Galgani’s Change of Variables in Differential Systems

  • Michel Rapaport
Conference paper
Part of the NATO Advanced Study Institutes Series book series (ASIC, volume 82)


After having extended to the non-canonical case an algorithm proposed by Giorgelli-Galgani (1978), we show that the generator of their transformation is similar to the generator of Deprit’s algorithm.

If \(\overrightarrow T = {\sum\limits_{i = 1} {{\varepsilon ^i}\overrightarrow T } _i}S\) and \(\overrightarrow W = {\sum {n{\varepsilon ^{n - 1}}\overrightarrow w } ^{(n)}}\) are respectively their expressions, we have\(\overrightarrow {{T_i}} = {\overrightarrow W ^i}\) for any n.

Copyright information

© D. Reidel Publishing Company 1982

Authors and Affiliations

  • Michel Rapaport
    • 1
  1. 1.FloiracFrance

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