Develops sufficient conditions for integrable systems to descend under Poisson reductions of generalized Hamiltonian torus actions, with applications to systems on doubles of compact Lie groups and moduli spaces of flat connections.
Degenerately Integrable Systems
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abstract
The subject of this paper is degenerate integrability in Hamiltonian mechanics. It starts with a short survey of degenerate integrability. The first section contains basic notions. It is followed by a number of examples which include the Kepler system, Casimir models, spin Calogero models, spin Ruijsenaars models, and integrable models on symplectic leaves of Poisson Lie groups. The new results are degenerate integrability of relativistic spin Ruijsenaars and Calogero-Moser systems and the duality between them.
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math-ph 1years
2025 1verdicts
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Integrable systems from Poisson reductions of generalized Hamiltonian torus actions
Develops sufficient conditions for integrable systems to descend under Poisson reductions of generalized Hamiltonian torus actions, with applications to systems on doubles of compact Lie groups and moduli spaces of flat connections.