Notes on the degenerate integrability of reduced systems obtained from the master systems of free motion on cotangent bundles of compact Lie groups

2023/09/28 by L. Fehér, Feher, L.
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2309.16245

openalex publication_date 2023/09/28 · openalex created_date 2023/10/01 · openalex updated_date 2026/07/28

Abstract

The reduction of the `master system' of free motion on the cotangent bundle T^*G of a compact, connected and simply connected, semisimple Lie group is considered using the conjugation action of G. It is proved that the restriction of the reduced system to the smooth component of the quotient space T^*G/G, given by the principal orbit type, inherits the degenerate integrability of the master system. The proof can be generalized easily to other interesting examples of Hamiltonian reduction.

Related

• Reduction and Integrability
• Degenerately Integrable Systems
• Reductions of Dynamics on Second Iterated Bundles of Lie Groups
• Hamilton-Jacobi Theorems for Regular Reducible Hamiltonian Systems on a Cotangent Bundle
• Integrable Hamiltonian systems on symmetric spaces: Jacobi, Kepler and Moser