- 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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