Characterization of toric systems via transport costs

TL;DR

This paper characterizes integrable Hamiltonian systems with torus actions by their zero transport costs relative to the time-$T$ map, providing a new criterion for such systems based on transport cost properties.

Contribution

It introduces a novel characterization of completely integrable Hamiltonian systems through the concept of transport costs associated with the torus action.

Findings

Systems with zero transport costs correspond to integrable Hamiltonian systems.

Provides a new perspective linking transport costs and Hamiltonian integrability.

Characterizes the structure of systems with effective torus actions.

Abstract

We characterize completely integrable Hamiltonian systems inducing an effective Hamiltonian torus action as systems with zero transport costs w.r.t. the time-$T$ map where $T \in {\mathbb R}^n$ is the period of the acting $n$-torus.