We prove that two simple, closed, real-analytic curves in C2n that are polynomially convex are equivalent under the group of symplectic holomorphic automorphisms of C2n if and only if the two curves have the same action integral. Every two simple real-analytic arcs in C2n are so equivalent.
Math Subject Classification32M05 53C12
Key Words and PhrasesSymplectic holomorphic maps Hamiltonian fields action
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