Symplectic homology of convex domains and Clarke’s duality

Abstract

We prove that the Floer complex associated with a convex Hamiltonian function on ${\mathbb{R}}^{2n}$ is isomorphic to the Morse complex of Clarke’s dual action functional associated with the Fenchel-dual Hamiltonian. This isomorphism preserves the action filtrations. As a corollary, we obtain that the symplectic capacity from the symplectic homology of a convex domain with smooth boundary coincides with the minimal action of closed characteristics on its boundary.