We define the symplectic displacement energy of a non-empty subset of a compact symplectic manifold as the infimum of the Hoferlike norm  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 .
All Science Journal Classification (ASJC) codes
- Geometry and Topology