The symplectic displacement energy

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Abstract

We define the symplectic displacement energy of a non-empty subset of a compact symplectic manifold as the infimum of the Hoferlike norm [4] 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 [3].

Original languageEnglish (US)
Pages (from-to)69-83
Number of pages15
JournalJournal of Symplectic Geometry
Volume16
Issue number1
DOIs
StatePublished - Jan 1 2018

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

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