Characterization of toric systems via transport costs

Hohloch Sonja

doi:10.3934/jgm.2020027

Article Contents

2020, Volume 12, Issue 3: 447-454. Doi: 10.3934/jgm.2020027

This issue Previous Article Some remarks about the centre of mass of two particles in spaces of constant curvature Next Article Angular momentum coupling, Dirac oscillators, and quantum band rearrangements in the presence of momentum reversal symmetries

Characterization of toric systems via transport costs

Hohloch Sonja

Department of Mathematics, University of Antwerp, Middelheimlaan 1, B-2020, Antwerp, Belgium

Received: September 2019

Revised: June 2020

Early access: September 7, 2020

Published online: September 7, 2020

The author was partially supported by the FWO-EoS project G0H4518N and the UA-BOF project with Antigoon-ID 31722.

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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.

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Mathematics Subject Classification: Primary: 28A75, 37J35, 49K21, 49Q10, 53D99, 70H05, 70H06.

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