Abstract
We use classical definitions and results of differential geometry in studying properties of transformations depending on a small parameter, acting on differential systems.
Notions of one-parameter Lie's group of transformations, of bracket of vector fields (Lie's derivative) ard used. In the same way, the notion of symplectic manifold and of transformations which keep invariant a 2-form are useful.
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Proceedings of the Sixth Conference on Mathematical Methods in Celestial Mechanics held at Oberwolfach (West Germany) from 14 to 19 August, 1978.
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Rapaport, M. Resolution methods of perturbed differential equations, using tools of differential geometry. Celestial Mechanics 21, 177–182 (1980). https://doi.org/10.1007/BF01230895
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DOI: https://doi.org/10.1007/BF01230895