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Let $(M,\omega)$ be an aspherical symplectic manifold, which is closed orconvex. Let $U$ be an open set in $M$, which admits a circle action generatedby an autonomous Hamiltonian $H \in C^\infty(U)$, such that each orbit of thecircle action is not contractible in $M$. Under these assumptions, we provethat the Hofer-Zehnder capacity of $U$ is bounded by the Hofer norm of $H$. Theproof uses a variant of the energy-capacity inequality, which is proved by thetheory of action selectors.

Hofer-Zehnder capacity and a Hamiltonian circle action with noncontractible orbits