Journal of Symplectic Geometry

Volume 16 (2018)

Number 1

The symplectic displacement energy

Pages: 69 – 83

DOI: https://dx.doi.org/10.4310/JSG.2018.v16.n1.a2

Authors

Augustin Banyaga (Department of Mathematics, Pennsylvania State University, University Park, Penn., U.S.A.)

David Hurtubise (Department of Mathematics and Statistics, Pennsylvania State University, Altoona, Penn., U.S.A.)

Peter Spaeth (GE Global Research, Niskayuna, New York, U.S.A.; and Department of Mathematics and Statistics, Pennsylvania State University, Altoona, Penn., U.S.A.)

Abstract

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.

Received 17 January 2014

Accepted 31 October 2017

Published 20 April 2018