Energy capacity inequalities via an action selector

Urs Frauenfelder; Viktor Ginzburg; Felix Schlenk

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Energy capacity inequalities via an action selector

Urs Frauenfelder·Viktor Ginzburg·Felix Schlenk

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Abstract

An action selector associates, in a suitable way, to each compactly supported Hamiltonian on a symplectic manifold an action value of the Hamiltonian. Action selectors are known to exist for a broad class of symplectic manifolds. We show how the existence of an action selector leads to sharp energy capacity inequalities between the Gromov width, the Hofer--Zehnder capacity, and the displacement energy. We also obtain sharp lower bounds for the smallest action of a closed characteristic on contact type hypersurfaces.

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Urs Frauenfelder, Viktor Ginzburg, Felix Schlenk. 2004-07-24. Energy capacity inequalities via an action selector. https://arxiv.org/abs/math/0402404

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