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

Abstract

Let $(M,\omega )$ be an aspherical symplectic manifold, which is closed or convex. Let $U$ be an open set in $M$, which admits a circle action generated by an autonomous Hamiltonian $H\in C^{\infty }(U)$, such that each orbit of the circle action is not contractible in $M$. Under these assumptions, we prove that the Hofer-Zehnder capacity of $U$ is bounded by the Hofer norm of $H$. The proof uses a variant of the energy-capacity inequality, which is proved by the theory of action selectors.

arXiv comment6pages

References in corpus (2)

• Functors and Computations in Floer homology with Applications Part II
• Hofer-Zehnder capacity of unit disk cotangent bundles and the loop product

Cited by in corpus (4)

• On the existence of periodic orbits for magnetic systems on the two-sphere
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• Function theoretical applications of Lagrangian spectral invariants