We say that a subset of a symplectic manifold is symplectically (neighbourhood) excisable if its complement is symplectomorphic to the ambient manifold, (through a symplectomorphism that can be chosen to be the identity outside an arbitrarily small neighbourhood of the subset). We use time-independent Hamiltonian flows, and their iterations, to show that certain properly embedded subsets of noncompact symplectic manifolds are symplectically neighbourhood excisable: a ray, a Cantor brush, a box with a tail, and -- more generally -- epigraphs of lower semi-continuous functions; as well as a ray with two horns, and -- more generally -- open-rooted finite trees.
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