In this paper, we prove that the Ekeland-Hofer capacities coincide on all star-shaped domain in $\mathbb{ R}^{ 2n}$ with the equivariant symplectic homology capacities defined by the first author and Hutchings, answering a 35 years old question. Along the way, we prove that given a Hamiltonian $H$, the (equivariant) Floer homology of $H$ is chain-complex isomorphic to the Morse homology of the Hamiltonian action functional.
Categories: math.SG