Resolution methods of perturbed differential equations, using tools of differential geometry
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 oneparameter 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 2form are useful.
 Publication:

Celestial Mechanics
 Pub Date:
 February 1980
 DOI:
 10.1007/BF01230895
 Bibcode:
 1980CeMec..21..177R
 Keywords:

 Differential Geometry;
 Lie Groups;
 Transformations (Mathematics);
 Celestial Mechanics;
 Differential Equations;
 Hamiltonian Functions;
 Astronomy