Answer by Thomas Rot for Symplectic diffeomorphism of the cylinder moving a...
The symplectic group acts (n)-transitively on connected manifolds of dim $\geq 2$. See Michor and Vizmann-Transitivity of certain diffeomorphism...
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I am currently reading though part of Zehnder's Lectures on Dynamical Systems. In Chapter VII, I have found myself in the following situation:$Z(1)$ is a subset of standard symplectic space...
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