Resolution methods of perturbed differential equations, using tools of differential geometry

Mathematics – Differential Geometry

Scientific paper

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

Scientific paper

Classical definitions and results of differential geometry are used in studying properties of transformations depending on a small parameter, acting on differential systems. A one-parameter Lie group of transformations and the bracket of vector fields (Lie's derivative) are employed, as well as the symplectic manifold and transformations which keep a 2-form invariant. Emphasis is given to transport diffeomorphism and the canonical transformation.

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