The symplectic displacement energy

Abstract

We define the symplectic displacement energy of a non-empty subset of a compact symplectic manifold as the infimum of the Hofer-like norm [5] of symplectic diffeomorphisms that displace the set. We show that this energy (like the usual displacement energy defined using Hamiltonian diffeomorphisms) is a strictly positive number on sets with non-empty interior. As a consequence we prove a result justifying the introduction of the notion of strong symplectic homeomorphisms [4].