The symplectic displacement energy
Symplectic Geometry
2019-11-18 v3 Differential Geometry
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].
Cite
@article{arxiv.1312.3924,
title = {The symplectic displacement energy},
author = {Augustin Banyaga and David E. Hurtubise and Peter Spaeth},
journal= {arXiv preprint arXiv:1312.3924},
year = {2019}
}
Comments
15 pages, 1 figure