From a Reeb orbit trap to a Hamiltonian plug

TL;DR

This paper introduces a straightforward method to construct a Hamiltonian plug on high-dimensional hypersurfaces by extending a trap designed for Reeb orbits, facilitating control over Hamiltonian dynamics.

Contribution

It provides a novel, simplified construction of Hamiltonian plugs using Reeb orbit traps, advancing techniques in symplectic and contact topology.

Findings

Constructed a Hamiltonian plug from Reeb orbit traps

Applicable to hypersurfaces of dimension five or higher

Simplifies previous complex constructions

Abstract

We present a simple construction of a plug for Hamiltonian flows on hypersurfaces of dimension at least five by doubling a trap for Reeb orbits.