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In the case of $\mathbb{R}^{2n}$ the exponential map just becomes $$ exp_{p}(v) = p + v$$ which results in $$ Dexp_{p}(w)_{v} = w $$ and proves that this map is a symplectomorphism.

I am wondering if this is also the case in a general symplectic manifold and in the likely event that it isn't true what possible properties are necessary to prove it is a symplectomorphism.

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  • $\begingroup$ see Lectures on Symplectic Geometry-Ana Cannas da Silva 4.2 $\endgroup$ – Bey Alexander Oct 30 '18 at 19:20
  • $\begingroup$ @BeyAlexander The mentioned reference gives a property for a general symplectomorphism, I am wondering if their is one more specificly for exponential maps? $\endgroup$ – Netivolu Oct 30 '18 at 19:50

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