99-100 Haro A.
Interpolation of an exact symplectomorphism by a Hamiltonian flow (38K, Latex 2e) Apr 6, 99
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Abstract. Let O be the zero-section of the cotangent bundle T*M of a real analytic manifold M. Let F:(T*M,O) -> (T*M,O)$ be a real analytic local diffeomorphism preserving the canonical symplectic form on T*M, given by the differential of the Liouville form a= p dq. Suppose that F*a-a is an exact form dS. Then: - We can reconstruct F from S and the dynamics on the zero section, f. - F can be included into a Hamiltonian flow, provided f is included into a flow. The proofs are constructive. They are related with a derivation on the Lie algebra of functions (endowed with the Poisson bracket).

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