Action-Angle variables on Dirac manifolds

2012/04/17 by Nguyen Tien Zung, Zung, Nguyen Tien
Mathematics · Physics and Astronomy · #37G05 #37J35 #70H06 #70H45 #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1204.3865

openalex publication_date 2012/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The main purpose of this paper is to show the existence of action-angle variables for integrable Hamiltonian systems on Dirac manifolds under some natural regularity and compactness conditions, using the torus action approach. We show that the Liouville torus actions of general integrable dynamical systems have the structure-preserving property with respect to any underlying geometric structure of the system, and deduce the existence of action-angle variables from this property. We also discover co-affine structures on manifolds as a by-product of our study of action-angle variables. 22 pages.

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