Uniqueness of generating Hamiltonians for topological Hamiltonian flows

TL;DR

This paper proves the uniqueness of the generating Hamiltonian for topological Hamiltonian flows within a specific function space, resolving an open question and enhancing prior results in the field.

Contribution

It establishes the uniqueness of the $L^{(1, fty)}$ generating Hamiltonian for topological Hamiltonian flows, answering an open question and improving earlier findings.

Findings

Proved the uniqueness of the generating Hamiltonian in the $L^{(1, abla)}$ space.

Resolved an open question posed by Oh and Muller.

Enhanced previous results by Viterbo on Hamiltonian flows.

Abstract

We prove that a topological Hamiltonian flow as defined by Oh and Muller, has a unique $L^{(1,\infty)}$ generating topological Hamiltonian function. This answers a question raised by Oh and Muller, and improves a previous result of Viterbo.